{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[![Dataflowr](https://raw.githubusercontent.com/dataflowr/website/master/_assets/dataflowr_logo.png)](https://dataflowr.github.io/website/)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "j5yGqm4Nl39f"
   },
   "source": [
    "Code adapted from [Optimization chapter](http://www.d2l.ai/chapter_optimization/) of Dive into Deep Learning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "4gJMsVnYl39r"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "def show_trace_2d(f, res , color = 'red'):\n",
    "    \"\"\"Show the trace of 2d variables during optimization.\"\"\"\n",
    "    x1, x2 = zip(*res)\n",
    "    plt.plot(x1, x2, '-o', color=color)\n",
    "    x1 = np.arange(-5.5, 3.5, 0.1)\n",
    "    x2 = np.arange(min(-3.0, min(x2) - 1), max(1.0, max(x2) + 1), 0.1)\n",
    "    x1, x2 = np.meshgrid(x1, x2)\n",
    "    plt.contour(x1, x2, f(x1, x2), colors='blue')\n",
    "    plt.xlabel('x1')\n",
    "    plt.ylabel('x2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "k2TDCgM3l399"
   },
   "outputs": [],
   "source": [
    "def train_2d(trainer):\n",
    "    \"\"\"Optimize the objective function of 2d variables with a customized trainer.\"\"\"\n",
    "    \"\"\"trainer(x1,x2,s_x1,s_x2) should return the updated positions x1, x2 and possible memory terms.\"\"\"\n",
    "    x1, x2 = -5, -2\n",
    "    s_x1, s_x2 = 0, 0\n",
    "    res = [(x1, x2)]\n",
    "    for i in range(20):\n",
    "        x1, x2, s_x1, s_x2 = trainer(x1, x2, s_x1, s_x2)\n",
    "        res.append((x1, x2))\n",
    "    print('epoch %d, x1 %f, x2 %f' % (i+1, x1, x2))\n",
    "    return res"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "KlFPt-C9l3-N"
   },
   "source": [
    "# Gradient descent\n",
    "\n",
    "[Video timestamp](https://youtu.be/UvM0hK4E2dc?t=589)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "UVnxAGegl3-R"
   },
   "outputs": [],
   "source": [
    "eta = 0.4\n",
    "\n",
    "def f_2d(x1, x2):\n",
    "    return 0.1 * x1 ** 2 + 2 * x2 ** 2\n",
    "\n",
    "def gd_2d(x1, x2, s1, s2):\n",
    "    return (x1 - eta * 0.2 * x1, x2 - eta * 4 * x2, 0, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 297
    },
    "colab_type": "code",
    "id": "npaYk5WUl3-e",
    "outputId": "f27bad51-3718-4da0-9421-7265248bdcd1"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 20, x1 -0.943467, x2 -0.000073\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_trace_2d(f_2d, train_2d(gd_2d))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 297
    },
    "colab_type": "code",
    "id": "7VfX0pq7l3-q",
    "outputId": "daa4cfd0-d362-41f5-e9e6-77435225d801"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 20, x1 -0.387814, x2 -1673.365109\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eta = 0.6\n",
    "show_trace_2d(f_2d, train_2d(gd_2d))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "pcsKwAyRl3-y"
   },
   "source": [
    "# Momemtum\n",
    "\n",
    "[Video timestamp](https://youtu.be/UvM0hK4E2dc?t=734)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "8qnyJQwnl3-0"
   },
   "outputs": [],
   "source": [
    "eta, gamma = 0.4, 0.5\n",
    "\n",
    "def momentum_2d(x1, x2, v1, v2):\n",
    "    v1 = gamma * v1 + eta * 0.2 * x1\n",
    "    v2 = gamma * v2 + eta * 4 * x2\n",
    "    return x1 - v1, x2 - v2, v1, v2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 297
    },
    "colab_type": "code",
    "id": "pT8vz7dKl3-7",
    "outputId": "f11697ca-5287-4dd9-8068-71e457f4e815"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 20, x1 -0.062843, x2 0.001202\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_trace_2d(f_2d, train_2d(momentum_2d))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 297
    },
    "colab_type": "code",
    "id": "qylwkBDBl3_C",
    "outputId": "0d1d51e5-778c-412b-bbae-9b7e31ec5595"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 20, x1 0.007188, x2 0.002553\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eta = 0.6\n",
    "show_trace_2d(f_2d, train_2d(momentum_2d))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 297
    },
    "colab_type": "code",
    "id": "fSZCrah6l3_K",
    "outputId": "2b006204-3c66-4d9c-c9f1-03ff12ed8483"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 20, x1 -0.589111, x2 0.698505\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eta, gamma = 0.05, 0.9\n",
    "show_trace_2d(f_2d, train_2d(momentum_2d))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "6WjZp2WPl3_T"
   },
   "source": [
    "# Nesterov accelerated gradient\n",
    "\n",
    "[Video timestamp](https://youtu.be/UvM0hK4E2dc?t=938)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "s02JrcZRl3_V"
   },
   "outputs": [],
   "source": [
    "eta, gamma = 0.05, 0.9\n",
    "\n",
    "def Nesterov_2d(x1, x2, v1, v2):\n",
    "    v1 = gamma * v1 + eta * 0.2 * (x1 - gamma * v1)\n",
    "    v2 = gamma * v2 + eta * 4 * (x2 - gamma * v2)\n",
    "    return x1 - v1, x2 - v2, v1, v2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 315
    },
    "colab_type": "code",
    "id": "upxkjOqIl3_b",
    "outputId": "e48007f6-069b-4ead-e4e8-fa06ccfc8d4e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 20, x1 -0.751356, x2 0.071637\n",
      "epoch 20, x1 -0.589111, x2 0.698505\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_trace_2d(f_2d, train_2d(Nesterov_2d))\n",
    "show_trace_2d(f_2d, train_2d(momentum_2d), color= 'green')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "RyzF7aAXl3_h"
   },
   "source": [
    "# Adagrad\n",
    "\n",
    "[Video timestamp](https://youtu.be/UvM0hK4E2dc?t=1080)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "-Mk4sixgl3_i"
   },
   "outputs": [],
   "source": [
    "import math\n",
    "\n",
    "def adagrad_2d(x1, x2, s1, s2):\n",
    "    # The first two terms are the independent variable gradients\n",
    "    g1, g2, eps = 0.2 * x1, 4 * x2, 1e-6\n",
    "    s1 += g1 ** 2\n",
    "    s2 += g2 ** 2\n",
    "    x1 -= eta / math.sqrt(s1 + eps) * g1\n",
    "    x2 -= eta / math.sqrt(s2 + eps) * g2\n",
    "    return x1, x2, s1, s2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 297
    },
    "colab_type": "code",
    "id": "TVc4sPtFl3_o",
    "outputId": "e74c06ce-f86a-42c7-8822-9313ff5a07e1"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 20, x1 -2.382563, x2 -0.158591\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eta = 0.4\n",
    "show_trace_2d(f_2d, train_2d(adagrad_2d))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 297
    },
    "colab_type": "code",
    "id": "XY90pzoLl3_v",
    "outputId": "4ac7254c-9ebb-4de2-f50e-02724cd5655b"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 20, x1 -0.002295, x2 -0.000000\n"
     ]
    },
    {
     "data": {
      "image/png": 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UFRUhsYW5AImJie16fFta+ntHPsrfH3juOdtfU1fefP55z06CAOn/Cy/IsfWKoq5+n87uS2e/f3ueb89jbX3NURISeL6fCB6UCAUFBSEzMxNr1qxpus9kMmHNmjUYO3aszeeMHTvW4vEA8O2337b4+LawIkTNlJdLa/3HKiUF+Ogj4IorXN8nZ7jiCnk/3bpZ3q/H+3R2Xzr7/dvz/NYe+/HHEtZfi42VMNfexC8hQSZ2ExE86qqx999/H9OnT8cbb7yBUaNG4fnnn8cHH3yAffv2ISEhAdOmTUO3bt2wePFiAMCGDRswfvx4PPnkk7jooouwYsUKPPHEE9i2bRsGDRpk12uqs86BMowZE4EW5mWTLyotBfr2lRV8n3kGGDHCPVZcdiauLO2c53NlaSKHs/eqMY9KhADg5ZdfxjPPPIPCwkIMGzYML774IkaPHg0AmDBhArp3745ly5Y1Pf7DDz/EQw89hMOHD6NPnz54+umnceGFF9r9euaJUGpqBI4edfAbIs91zz1ymiMjA9ixQ3blJSIit+C1iZCrmSdC/v4RqK31zoE+tVNWFjB0qIyyv/kG+P3v9e4RERGZsTcR8pg5Qnrz85O/ecXFeveEdKcowF/+Iv8hLr+cSRARkQdjImQndTmiw4d17Qa5g08+AdasAYKDgWef1bs3RETUCUyE7DR0qLTusiAs6aSqClAX3Jw/XyafEhGRx2IiZKdLLpH244/17Qfp7OmngaNHgbQ04P779e4NERF1EhMhO11wARAQIPsTHjigd29IF4cPA089JcfPPguEhOjaHSIi6jwmQnaKidE2Gv/kE337QjqZNw+oqZH/CFdeqXdviIjIAZgItYP6t4+nx3zQd99JBuzvD7z4ovO2PSAiIpdiItQOl10mf/82bwYXVvQl9fXAn/8sx3fdBdi5KjkREbk/JkLtkJCgrW7P02M+5OWXgb17gbg44JFH9O4NERE5EBOhduLpMR9TVAT87W9yvHgxEBWlZ2+IiMjBmAi10+WXS/vzz7LfIXm5hQtlh/kRI4Bbb9W7N0RE5GBMhNopNRUYM0Z2WXjxRb17Q07166/A0qVy/NJLss8KERF5FX6yd8ADD0j7/PPAsWO6doWcxWQC7r5bjqdPl+yXiIi8DhOhDvjDH4Dx42VJmYce0rs35BRvvSWXB4aHA08+qXdviIjISZgIdYDBADzzjBy/8w6wfbuu3SFHKysDFiyQ40WLgMREfftDREROw0Sog0aOBK67TuYKzZ+vd2/Iof72N6C4GMjIAGbP1rs3RETkREyEOuHxx4HAQODbb4Gvv9a7N+QQe/bIxGgAeOEFIChI3/4QEZFTMRHqhJ49tfm0990HNDbq2x/qJEWRFaQbG2UZ8fPP17tHRETkZEyEOumhh2SNvV27ZL4QebBPPwXWrAGMRtldnoiIvB4ToU6KidEup3/oIaCqSt/+UAdVVQFz58rx/PlS7iMiIq/HRMgBZs8G0tOBvDxuReWxnnkGOHJEVsxUrxgjIiKvx0TIAYKDgX/8Q46ffhpYuVLf/lA7HT6srRX07LNASIiu3SEiItdhIuQgV1wh82wBYNo0YP9+fftD7XDvvbI65sSJwFVX6d0bIiJyISZCDrRkCXDOObJH5xVXAGfO6N0jatOaNcDHHwP+/rJ5nMGgd4+IiMiFmAg5UGAg8MEHshBxVhbwxz/KFdnkpurrtTLeXXcBgwbp2x8iInI5JkIOlpQEfPghEBAAvP++rMlHbuqVV2QBxbg4WU2aiIh8DhMhJzjnHG0ZmnvvBX74Qd/+kA1FRbKPGAAsXgxER+vbHyIi0gUTISeZPRu44QZZpPiaa4D8fL17RBYeeEAmc2VmArfcondviIhIJ0yEnMRgAP75T2DwYCk+XHUVUFurd68IAPDrr8Cbb8rxSy/JRGkiIvJJTIScKDQU+OQT2YJj40bgT3/i5GndmUzajvLTpgFjx+rbHyIi0hUTISfr3Rt47z2pEL35JjBrlvwtJp289ZZUhMLDtUUUiYjIZzERcoELLpAkyGAA3nhDLqvnTvU6KCvTts94+GG5xI+IiHwaEyEXmTFDdqf38wOWLgWmTwcaGvTulY955BGguBjo109bP4iIiHwaEyEXuvFGYMUKWWPo3XflqrL6er175SP27JGJ0YCsIB0UpG9/iIjILTARcrGrrwY++khWof7wQ+DKK2WbK3IiRQH+8hcpwV16KXD++Xr3iIiI3AQTIR1ceqnsUB8cDKxaBVx8MVBZqXevvNhnnwHffQcYjcA//qF3b4iIyI14TCJ06tQp3HjjjYiIiEBUVBRuu+02nGljV9MJEybAYDBYxJ133umiHrfugguA//5XLrH/7jtgyhSZy0sOVl0NzJ0rx/fdB/TsqW9/iIjIrXhMInTjjTciKysL3377Lb744gv88MMPuP3229t83syZM1FQUNAUTz/9tAt6a58JEyQJiowEfv4ZmDQJOHlS7155maefBg4fBlJTgYUL9e4NERG5GY9IhPbu3YuvvvoK//73vzF69Gicc845eOmll7BixQrkt7F3RUhICBITE5siIiLCRb22z5gxwNq1su/n1q2SHBUW6t0rL3HkiLZW0JIlQEiIvv0hIiK34xGJ0MaNGxEVFYURI0Y03Td58mT4+flh06ZNrT733XffRVxcHAYNGoSFCxeiqqqq1cfX1taivLzcIpxt+HDZmDUpCdi9Gxg9GmjjbZE95s2TmegTJsgsdSIiIisekQgVFhaia9euFvcFBAQgJiYGha2UT2644QYsX74ca9euxcKFC/HOO+/gpptuavW1Fi9ejMjIyKZITU11yHtoS//+wI8/An36AEePAueeC7z8Mrfk6LA1a4CPP5Z9xF58UVazJCIisqJrIrRgwYJmk5mtY9++fR3+/rfffjumTJmCwYMH48Ybb8Tbb7+NTz/9FLm5uS0+Z+HChSgrK2uKY8eOdfj126tXL2DLFtmgtb5etsS6/nqgosJlXfAO9fXagol/+pPsfEtERGRDgJ4vPm/ePMyYMaPVx/Ts2ROJiYkoLi62uL+hoQGnTp1CYmKi3a83evRoAEBOTg569epl8zFGoxFGo9Hu7+loERHABx8AL7wgFzm9/z6wfbsUNwYO1K1bnuXVV2UBxbg4WU2aiIioBbomQvHx8YiPj2/zcWPHjkVpaSm2bt2KzMxMAMD3338Pk8nUlNzYY/v27QCAJDffY8pgAObMAUaNAq69FsjOluPXXpMN06kVxcXAokVy/MQTQHS0vv0hIiK35hFzhPr374+pU6di5syZ+PXXX/Hzzz/j7rvvxnXXXYfk5GQAQF5eHjIyMvDrr78CAHJzc/Hoo49i69atOHz4MD7//HNMmzYNv/vd7zBkyBA9347dxo0Dtm0Dfv97oKpK9ie75RYuvtiqBx6QBZkyM4Fbb9W7N0RE5OY8IhEC5OqvjIwMTJo0CRdeeCHOOecc/POf/2z6en19PbKzs5uuCgsKCsJ3332H888/HxkZGZg3bx6uvPJKrFq1Sq+30CHx8bLw4qOPyoaty5ZJdWjPHr175oY2bwbefFOOX3pJJkoTERG1wqAovC6pNeXl5YiMjERZWZnuaxCtWyeTpwsLZUmcV1+VKhEBMJmkhLZpk5w/fOstvXtEREQ6svfvt8dUhEiWw9m+HZg8WU6VzZgh0cZOI77h7bclCQoP1xZRJCIiagMTIQ+TkAB89ZV2quytt4ARI4ANG/TumY7KyoAFC+T44YdlZUoiIiI7MBHyQP7+wEMPAd9/D3TrJleVnX02cMcdwOnTevdOB3//O1BUBPTrp60fREREZAcmQh5s/Hhgxw7t4qh//hPIyADefdeHVqTeu1dWjgaA558HgoJ07Q4REXkWJkIeLjYW+M9/gPXrZZuO4mLgpptkHtHevXr3zskURSpADQ3AJZcAU6fq3SMiIvIwTIS8xO9+JxOpH38cCA6W02ZDh8qyOl677tBnnwHffQcYjcBzz+ndGyIi8kBMhLxIUJAkPnv2AH/4g2y5tXgxMGAAsHKll50uq64G5s6V43vvBXr21Lc/RETkkZgIeaEePYBVqyT5SU+X3ewvuwy4+GKglf1mPcszzwCHDwOpqcDChXr3hoiIPBQTIS92ySVSHXrgASAwEFi9WjZuffhhWYfIYx05IqUuAFiyBAgN1bc/RETksZgIebmQEJk3tHOn7FlWWytrEPXvD3zyiYeeLrv3XqCmRlaYvPpqvXtDREQejImQj8jIAL7+Gvj4YyAtTU6XXXmlXGi1b5/evWuH778HPvpIVpN88UXAYNC7R0RE5MGYCPkQgwG44gq5rP6hh2Ry9TffyOmyadOAAwf07mEb6uu1BRP/9Cdg8GB9+0NERB6PiZAPCgmR02NZWcCll8p+pe+8I6fLZsxw4wnVr70mnY6NldWkiYiIOomJkA/r3VuW4tm8GbjoIqCxUfYu69dPVqt2q4SouFhmeQPAE08A0dH69oeIiLwCEyHCiBHAF1/I5u1Tp0pCtHSpJEQzZgD79+vdQ8ilb2VlwFlnAbfdpndviIjISzARoiajRgH//S+wcSNwwQVahah/f9m2Q7dJ1Zs3A2++KccvvSS7zhIRETkAEyFqZswY4MsvgV9/lRWqTSbZyHXAAOC66+RSfJcxmYDZs+U6/5tvBsaNc+GLExGRt2MiRC0aOVJWqN66VVamVhTg/fdlD7NLLpFTaU73zjvyQmFhwFNPueAFiYjIlzARojaddRbw6afAjh3AtdfKZfirVknl6Pe/B9atc9LCjGVlwP33y/HDDwNJSU54ESIi8mVMhMhuQ4YAK1bIOkQzZgABAbL5+8SJwNlnA59/LmeyHObRR4GiIqBvX+Avf3HgNyYiIhJMhKjd+vWTq8oOHABmzQKMRplgfemlkiy98QZw5kwnX2TvXuCFF+T4hRdk9UciIiIHYyJEHda9O/Dqq7IJ/P33A+Hhst7hnXcCycnA3XcDu3Z14BsrCjBnDtDQIJORpk51bMeJiIj+h4kQdVpiIvDkk7J/2XPPAX36ABUVwCuvSIXonHOA5ctln1S7rFwpe38YjcA//uHUvhMRkW9jIkQOExUlhZx9+ySPufJKWfLn55/lyvdu3YB584Ds7Fa+SXU1cM89cnzvvUCvXi7oORER+SomQuRwfn5yNdlHH0mV6NFHgdRU4NQpKfBkZAC/+51cGV9dbfXkJUvkXFtKCrBwoR7dJyIiH2JQFKdc+Ow1ysvLERkZibKyMkREROjdHY/V2Ah89RXw+uuyWKN6dVlUlKxaPXMmMCTyiCxjXV0tl6dde62ufSYiIs9l799vJkJtYCLkeMePy1Vn//kPcOSIdv+I6BzcdnoJrjv7OKJ+XCULFhEREXUAEyEHYSLkPCYT8O23wL/+BXy+0oT6BjlTG2w04aqr/XDrrcD48XKqjYiIqD3s/fvNPzGkGz8/YMoU4KMVDcjrNR7PYi4GRBegptYPy5cD550H9O4NPPIIcOiQ3r0lIiJvxESI9Pfqq4jP/glzY9/G7gNG/PKLzBkKD5cE6G9/A3r2lMTorbeA8nK9O0xERN6Cp8bawFNjTlZSIgsPlZXJktS33970paoq2eNs2TJgzRptP7OgIOD884GrrpL1FqOj9ek6ERG5L84RchAmQk42cybw73/Lzq6//ioLD9lw9Khcbr98uaxTpAoIACZNkjWLLrsMiI93TbeJiMi9MRFyECZCTrRlCzBqlJR6fvpJdm5tg6IAe/bIGkUff2y5hYefn6xifcUVwOWXA2lpTuw7ERG5NSZCDsJEyElMJkl8fvlFFhJ6550OfZv9+yUh+ugjYNs2y69lZkpCdOmlwMCBvBqfiMiXMBFyECZCTvL228D06UBYmOy5kZzc6W95+DDw2Wcyr+jHH7U5RYDs1HHppRLjxskpNSIi8l5MhByEiZATlJcDffsCRUXAU08B8+c7/CWKi4HPP5ekaM0aoLZW+1psLHDRRcDFF8uka/6zEhF5j+Ji2cEgP78cDz7IRKjTmAg5wX33yZ5iffvKJJ+gIKe+3JkzwNdfy6b2q1fLnmeqwEBgwgTgD3+QxKhHD6d2hYiIHExR5E/JF18Aq1YBmzbJfWFh5ThzxosSoccffxyrV6/G9u3bERQUhNLS0jafoygKFi1ahH/9618oLS3F2Wefjddeew19+vSx+3WZCDnYvn3A4MFAQ4Ok7Bdc4NKXb2iQedmrVkkcOGD59f79pVp04YUyhcnJORoREXVAZSXw/fcyuP3yS+DYMcuvn3UWcP755XjySS9KhBYtWoSoqCgcP34c//nPf+xKhJ566iksXrwYb731Fnr06IG//vWv2LVrF/bs2YPg4GC7XpeJkAMpCjB1KvDNN1J++fxzvXuE/fu1pOinn2RzWFV4uJw6u+AC6Xa3bvr1k4jIlymKDFy/+kqSn3XrgLo67evBwbKUysUXS4W/WzcvniO0bNkyzJkzp81ESFEUJCcnY968ebj33nsBAGVlZUhISMCyZctw3XXX2XxebW0tas0mlJSXlyM1NZWJkCOsXCmL/QQFAVlZsn+GGzl9WvY+W70a+O9/Za1Hc4MGyerW550ne6BFRenSTSIin1BQAKxdK7FmTfOtltLTpYJ/0UUyxSEkxPLr9iZC7bp2ZseOHVi1ahViYmJwzTXXIC4uzuIF58yZgzfffLM939JpDh06hMLCQkyePLnpvsjISIwePRobN25sMRFavHgxHnnkEVd103dUVwP33CPH997rdkkQICtUX3ONhMkEbN2qJUWbNwO7d0u8+KJcij9smPzyjR8PnHsuEBOj9zsgIvJc+fnA+vVS7Vm/Xi4oNhcYKJ+1F1wgyU9GhmOWRbG7IvTNN9/g4osvRp8+fVBRUYHKykp8+OGHmDhxIgCgqKgIycnJaDQ/t+AE9laENmzYgLPPPhv5+flISkpquv+aa66BwWDA+++/b/N5rAg5yWOPAX/9q9Qrs7OB0FC9e9QuJ07I+Wh1dGL9C2owAEOGaEnRuecCCQn69JWIyN0piix58uOPwA8/SOKTk2P5GIMBGD4cmDhRYvx4WXHFXg6vCP3tb3/Dvffei8cffxyKouCZZ57BJZdcgg8//BBTp061v2dmFixYgKeeeqrVx+zduxcZGRkd+v4dYTQaYTQaXfZ6PuHoUeCJJ+R4yRKPS4IAIC5OqxYBMnL54Qdt5LJvH7Bjh8SLL8pj+vTRkqJzzpG1jLioIxH5IpNJZkT8+KMWeXmWj/Hza15pd8VeknYnQllZWXjnf6v/GgwGzJ8/HykpKbjqqquwYsUKjBw5st0vPm/ePMyYMaPVx/Ts2bPd3xcAEhMTAUilyrwiVFRUhGHDhnXoe1IH3XefnBr73e+Aa6/VuzcOkZwMXHedBCBLIv3wgxa7dsnEvgMHAPVscUKCXImmxvDhvCqNiLxTZaVsH/nzzxIbN8re2uYCAoARIyThGT9eBoyRka7vq92JkNFobHY66oYbboCfnx+uvfZaPPvss+1+8fj4eMQ7aZfMHj16IDExEWvWrGlKfMrLy7Fp0ybMmjXLKa9JNqxdC3zwgaT66uQaL5SQAFx9tQQAlJbKL7868tmyRZKlTz6RAOQqhxEjgLFjtfhf/k5E5DHU01wbN2qxY4csV2IuNFQ+59RK+ejRzSc468HuRGjYsGFYu3YtMjMzLe6/7rrroCgKpk+f7vDOmTt69ChOnTqFo0ePorGxEdu3bwcA9O7dG2H/O2mYkZGBxYsX4/LLL4fBYMCcOXPw2GOPoU+fPk2XzycnJ+Oyyy5zal/pfxoagD//WY5nzQKGDtW3Py4UFaVdzQAANTWSDKmjow0bgJMn5ZL9n37Snte9OzBmjHxAjB4tVSM7V3ogInKJigq5gGTTJolffpGBnrWUFMsq+JAh7rm9kd1dmjVrFn744QebX7v++uuhKAr+9a9/Oaxj1h5++GG89dZbTbeHDx8OAFi7di0mTJgAAMjOzkaZWe1t/vz5qKysxO23347S0lKcc845+Oqrr+xeQ4g66bXX5DKr2Fjg73/Xuze6Cg6Wsu8558htRZE1jMxHULt3y6jq8GFgxQp5XGCg5I+jRwOjRkkFqV8/wN9fr3dCRL6kvl5O9W/eLKe6Nm0C9uyx3MsRkM+q4cMtK9xpafr0ub3avY7Q2rVrm64Us/bGG2/gjjvucEjH3AUXVOygkhLZQqO0FHj9dcDL/l84Q3m5fND88os20rJeywiQqyYyM4GRIyUxyszkRGwi6ryGBrnwY+tWSXw2b5ZTXOZ7NarS0rTK9Zgx8jnkbjUGpy2oaDQa8ec//xlPPPEEAgMDAQAnTpzALbfcgp9++gmnT5/uXM/dDBOhDrr9duBf/5IhwubNLGF0gHrefdMmSZA2bwa2bQOqqpo/NjJSftSZmRKDB0vl6H+/okREFqqqgL17gZ07JfHZulWSnurq5o+NitIGXmry4wnzGZ2WCG3YsAHTpk1DWFgY3nvvPRw6dAi33XYb+vbti3feeQfp6emd7rw7YSLUAVu2yHkcRZEJMGefrXePvEZDg3x4qaO1rVvlg8zWiC0wUJKhQYMkMRo0CBgwQDaWZV5K5Bvq6mR9nqwsOf2+a5e0OTnNT28BUnEePlySnpEjJTy14uzULTbOnDmDO++8Ex999BFMJhMeffRRzJ8/HwZP/Em1gYlQO5lMMhFm40bgxhuB5cv17pHXq6+Xc/bqqO633+SDrqLC9uODg2Vz2QEDgIED5bh/f/mwc8eJjETUtpoaWa5j7175PMjKknb//uZXb6ni4mSQdNZZEpmZsv6Zn59r++4sTtliQ7V//35s2bIFKSkpyM/PR3Z2NqqqqhDqgQvlkYMtXy5JUFgY8PTTevfGJ6gTqocOBW69Ve5TFNmNWR39qe2+ffKB+dtvEtbfp08fWba+f3+pJqmhx9oeRGRJUWTe4P79srp9drYkPnv3yj5cJpPt54WFycBHrQyrVeKuXT2z0uNo7a4IPfnkk1i0aBFuv/12PPPMM8jJycHNN9+M8vJyLF++HGPHjnVWX3XBilA7lJfLX83CQuCpp4D58/XuEVlpbAQOHtRGjFlZ8iGanW177pEqIUHmvvftK8mSGr16ucc6IETepLxcW5BVDTX5aW13qchIrcI7cKBW9U1N9c2Ex2mnxpKSkvDmm2/iggsuaLqvvr4eDzzwAF588UWLfbq8AROhdrjvPtlCo08fKUFwqxKPYTJJBWnvXqka7d2rffAWFLT+3JQUSYhshSuWxyfyNIoCFBcDubm2o7i45ecaDHLFllqtVSu4/fvLgMUXE56WOC0ROnHihMWu8+bWr1+P8ePHt6+nbo6JkJ327ZNaa0MD8OWXsj0weQV1dJqdLcnRgQMy0fLAAaCti0QjI2Vytnl07w6kp0vwV4q8kaIAp04BR45IHD4sldhDhyQOH269AgtIUqNWXnv3lmpsv35y3KWLK96F53PqZGlfwkTIDooiic/XXwN/+AOwapXePSIXOXlSEiLrEW1Oju2VZq1FR2tJUWqqRFqadpyczAnc5H5qa2XD0KNHpZJ67Jh2rCY+lZWtfw+DoXk1tXdvreWfm85jIuQgTITs8PnnwKWXyg6iWVnyW0w+r7JSWylbHQmro+EjR2TE3BY/PxkZp6QA3bppbXIykJSktdHRPCVAnWcyASdOyOng/HytPX5cEh+1tbXQqS0JCZLkd+/evDKalsbZA87m1KvGiJrU1AD33CPH8+YxCaImoaEyUXPgQNtfr6jQTh0cOaKNrNXRdV6eLA1QUCCxeXPLr2U0SkKUkCALvSUmasddu2oRH8+kydc0NkrSXVwsUVIi1cqiIrmuQw31dkuXmlsLDrZdxVQrnGlpPIXlKZgIUec8+6yc/O7WDXjgAb17Qx4kPFy7lNcWk0n+aB0/bjkiP35cS44KCuSPXG2tVn1qS0CArJ8SEyPb4MXEaMdRUZIoRUdrx1FRMtcpIkKukGMS5XqKApw5A5SVSZSWyvw06/bkSfn/cOqUdnzyZMuXlbeka1dJrNWqo3VFMiVF/s/w/4J3YCJEHXfsGPDEE3L8zDOyWAWRg6inxRISZKG3ltTUSEJkPqo3P1arAMXF8ke0oUF7THsFBEhCpCZG4eHNIzRUIixMOw4NlSSqSxdp1ePgYC08fS6UosjPtqZGi6oq2bKhqkqLykotzpzRjisqmkd5ufyblZe3P5mxFhNjWR00rxqqx2pVkVvT+BYP/9VznXnzgD/+UXaO4Cjgf+69Vz7Zzj0XuO46vXtDPio4WJt30ZbaWkmKSkpsVxDMqwvmxxUV8oe4oUF7vKP5+8spPjWCgiwjMFCSpYAAy2M/P3muGn5+EurnlMGghaLYjsZGCZNJO25o0KK+Xmvr6iyjtlaipsb2lg2O/hlFRlpW7syrd+YVPjW6dpX7mdxQSzhZug3qZCugDEAEMjKAadOAm2+W8qjPWrcOmDhRPnG3bZNljYm8lHpqRq1QlJVZVi3Mqxi2Kh5qNcS6OmLvfBRPFBRkuwrWUsVMrahZV9oiI7Xo0oUDUbIfrxpzEPUHec01ZVi1KqJpZ16DATjvPEmIrrhCfmF9RkODbEyzaxfwpz8Br7yid4+IPFJjo1ZNUduamuaVl9ra5pUZtTWZtEqOeQs0r/yYV4fMw7yapLbmlSfz1rpaFRhoeYpPrWh5y35V5LmYCDmI+Q8SiMBHHwFvvw2sX689JiQEuOwySYomT/b8c/1tevllYPZsqTsfOCAtERGRG2Ei5CAt/SAPHQLefRd45x1ZbVeVkABcf71svJ6Z6YVl3JISWeK0tBR47TXgzjv17hEREVEzTIQcpK0fpKIAv/4qCdGKFTLhUtWvnyREN94I9Ozpwk470x13AP/8JzBsGLBli9TRiYiI3AwTIQdpz8rSdXXAN98Ay5cDK1fKuX7VmDHADTcA11wjVSOPtHUrMHKkZH8//gicc47ePSIiIrKJiZCDdHSLjfJy4NNP5fTZmjXa5EU/P5lHdP31wCWXeND0GkUBzj4b2LhRSlzLl+vdIyIiohYxEXIQR+w1VlAAfPAB8N57chpN5e8vV6BffrlMtk5OdkyfneKdd2TdgNBQ2Ya8Wze9e0RERNQiJkIO4uhNV3NyZC7RBx/I1efmxoyRpOjyy4E+fTr9Uo5TUSETpAsLgSefBO6/X+8eERERtYqJkIM4c/f5nBw5ffbJJ8Avv1h+bcAA2dD9ssuAESN0XpNj/nzZQqNPH8neuGUyERG5OSZCDuLMRMhcfr5MsP7kE1m02XzF2eRkmU906aVyKs2leUh2NjB4sKzctno1cOGFLnxxIiKijmEi5CCuSoTMlZYCX34JfPYZ8N//yjL9qrAwYOpUSYwuusjJk60VRRKfr74C/vAHYNUqJ74YERGR4zARchA9EiFztbXA999LUrRqlUy8Vvn7y4VcF18seUq/fg5ewPHzz6UMFRQEZGUBvXs78JsTERE5DxMhB9E7ETJnMsn+pitXSo6yc6fl13v3loTo4otliZ+goE68WE0NMHAgcPAgsHAh8MQTneo7ERGRKzERchB3SoSsHT4MfPGFVIrWrZMFHVXh4cD558vpswsv7MAijo8/Djz0kFwmv2+fnJMjIiLyEEyEHMSdEyFzFRXAt99KUrR6tWwJZm7ECEmKLrhAjlvdGePYMSAjA6iqksWPrr/eqX0nIiJyNCZCDuIpiZA5k0m2AVu9WmLrVsuvx8YCkybJCte//z3QvbvVN7juOuD994FzzwXWr/fCnWOJiMjbMRFyEE9MhKwVFMjVZ//9r+yFVl5u+fWePSUxmjQJOC94A+IvO1sWLtq6VTZXJSIi8jBMhBzEGxIhc/X1ss3Hd99J/PKL5ZpFADAEO3DekBM477FJ+N3vgMhIffpKRETUUUyEHMTbEiFrFRXADz/IxrBrPjiBnXlxFl/38wPOOksWcpw4Ua5GCw/XqbNERER2YiLkIN6eCDU5cQLo2xclp/2x9rZ38X3A+Vi7Fti/3/Jh/v4y2XrCBGD8eCZGRETknpgIOYjPJEJ33gm88YbMCdqypemysrw8YO1aLQ4dsnyavz+QmQn87ndaYhQV5fLeExERWWAi5CA+kQht2yZlHkUBfvxRspkWHDkiF5KtWyftwYOWXzcYgKFDJTE691yJdq9hRERE1En2/v3Wc0/zdnn88ccxbtw4hISEIMrOksOMGTNgMBgsYurUqc7tqKdRFGD2bGlvuKHVJAgA0tOBadOAN98EcnMlMXr7beCPfwT69pVvs3078OKLwNVXA4mJcv9ttwHLlslzmHoTEZG78JiK0KJFixAVFYXjx4/jP//5D0pLS9t8zowZM1BUVISlS5c23Wc0GhEdHW3363p9RWj5cuDmm4HQUNlpvlu3Tn27ggIpKq1fL+3u3c0Tn8RE2SNNjeHDgcDATr0sERGRBXv/fge4sE+d8sgjjwAAli1b1q7nGY1GJCYmOqFHXqCiApg/X47V7TQ6KSkJuOYaCQA4fRrYsEGSoh9/BDZvBgoLgY8/lgCALl2A0aOBsWOBMWOAUaMkWSIiInI2j0mEOmrdunXo2rUroqOjcd555+Gxxx5DbGxsi4+vra1FbW1t0+1y69UHvcljj0kJp3dv4J57nPIS0dGytcdFF8ntmhqZi/3TT8DPP0uSdOqUzDlat057XmqqJEQjR0pkZnI9IyIicjyvToSmTp2KK664Aj169EBubi4eeOABXHDBBdi4cSP8W9hsa/HixU3VJ6+WnQ0895wcP/88YDS65GWDg2UakjoVyWSSPV03bAA2bpTFHrOyZLuzY8e0qhEgc41GjpR53ZmZckqNe8ESEVFn6DpHaMGCBXjqqadafczevXuRkZHRdHvZsmWYM2eOXXOErB08eBC9evXCd999h0mTJtl8jK2KUGpqqnfNEVIU2ZL+q6+kVPPFF3r3yEJFhVzItmmTVI+2bGl+2T4gV6hlZEhSpMawYVzXiIiIPGSO0Lx58zBjxoxWH9OzZ0+HvV7Pnj0RFxeHnJycFhMho9EIo4uqI7r54gtJgoKCtKqQGwkPlzWJxo/X7jtxQrY+27xZEqOtW4Hjx4G9eyWWL5fHGQxAnz6yGvZZZ0nVaPhw2WiWiIjImq6JUHx8POLj4132esePH8fJkyeRlJTkstd0OzU1wJw5cjx3rmQNHiAuDpgyRUJVVCQJkRrbtsnptP37JVas0B6bkiLVouHDpR02DOjeXbYQISIi79LQIFNg7eExc4SOHj2KU6dO4ejRo2hsbMT27dsBAL1790bY/yaKZGRkYPHixbj88stx5swZPPLII7jyyiuRmJiI3NxczJ8/H71798YU87+mvuYf/5BVEJOTgQcf1Ls3nZKQIGf4LrxQu6+kBPjtN4lt2yRycqR6dPy45VnA8HBgyBBZAFKNQYNkJQEiIvIMp08DO3cCO3ZokZUlA2B7eMw6QjNmzMBbb73V7P61a9diwoQJAACDwYClS5dixowZqK6uxmWXXYbffvsNpaWlSE5Oxvnnn49HH30UCe1Y6tir1hE6fhzo1w+oqgLefVcWUPQB5eXyS/Lbb7LY42+/yS9JXV3zxxoMQK9ewODBkiQNGSLHPXs27TpCREQ6qKuTav/OncCuXdLu3Cl/2mwJDy9HRQW32Og0r0qErr9ezhedc45sOW8w6N0j3dTXy4Vz5iOIHTvkdJstXboAAwZIxWjQIEmOBg6UpZd8+MdIRORwJpNcILN7txa7dslndkOD7eekpWmV/WHDpI2LK0d0NBOhTvOaRGj9etky3s9PJtQMG6Z3j9xScbHlSGPnTmDPHplaZUtEhCRIAwdKDBggkZLCBImIqDWNjZLw7N0rVXo19u0DqqttPyc8vHnFftAg25t9c9NVB/GKRKihQa4t37kTmDULePVVvXvkURobZVrVrl2Wo5MDB+RrtoSFybpHffvK2ch+/eS4Tx9JnoiIfIGiACdPyimtAwekqqNGTg5gtlqNBaNRlkdREx21Ep+aav8gk4mQg3hFIvTKK8DddwMxMfK/kdeSO4R6vjorS6pG6mgmJ6fl8i0gk7zVpKhPH1nYWw0uEElEnuj0aUl0cnIkDhyQ2L9fvtaS4GAZKKoVdbW67oh5mUyEHMTjE6ETJ+Sv7unTUgmaNUvvHnm9ujqpIJmPfNTRUEtzkFSJiTJZ21bExfF0GxHpw2SSy9Fzc7U4eFDanBzZKqk1qaky8DOvkvfrB6SnO+9CFI9YUJFc4KGHJAkaOhS4/Xa9e+MTgoKkpGu2IHqT8nJtlKSOntT2xAnZkLawUPZhsxYWBvToISMl87ZHD/kwYTWJiDqjtFTm7Bw+LO3BgxKHDkm0dBpLlZwslW210q0mPr16ASEhrngHHcOKUBs8uiL0228yN0hR5Cqxc8/Vu0fUitJSSYjMR1xqtHR5qLm4OEmKuneXxMg6uGktke9S5+ocOdI81OSnrKz17+HvL58lvXrJQEytVvfuLa27rcHGipCvUxRg9mxpr7+eSZAHiIqSDWVHjGj+tZoa+cBSR2fqSE0duZWWSkXpxAnZhsSWyEi5xDQtTcrU6nFKitzu1s1le+8SkYNVVmoLxx47Bhw9qrXqcWVl29+na1dJdnr2bF59Tk0FAgOd/15cjRWhNnhsRejdd4GbbpIUPTtb/sqR1yotlaRITYysR3xtnb9Xde0qiVFKivyXUUO9nZwsV71xrhKRayiK/P7m5dmOY8ck+WltQrK5hITm1WLzU+zuVtXpDFaEfFlFBXDffXL84INMgnxAVJS2h5otZ85IQnTsWPPRojqCrKmRdZSKi2VrkpaEhEhClJwMJCVJm5gox+ZtbCwTJqKWNDbKlkCFhTIJWZ0fWFAA5OdLqMe2VsG3JSxMqjYpKVrFV60Aq1Xg4GDnvi9PxETIGz3+uPwG9e4tG6uSzwsL0y5LtUUddapJ0fHjzUeex4/LHIKqKu0S2dYEBEiFKSHBMrp2bR7x8TLJnMiTVVdLcqMOKNQoKmoeJ07IlVj2iouzrNKqoSY+KSmcB9hRTIS8zf79srEqADz/PCd9kF0MBqngxMbKBYYtqaqyHLGqYT6aLSyUSZkNDdrX7RERIR/28fHSqhEbK0tgmUdUFBAdLc/x83PIj4CoSWOjnG4uLZVTTqdOWcbJk9qcvJIS7dieOTjmDAYZCJhXUhMTJcFRq61qxZUf5c7DRMjb3HOPbKR14YXARRfp3RvyMiEh2pUiramr00bChYWWI2HrEXNJifzhKS+XOHjQ/v74+ckoWE2M1GPzVo2ICInISFmm3zy4oa73qK+X2QFqqP+vysuloqm2ZWVasmN+fPq0PKajgoIsK53qsXVlNCFBvh7Av8K64z+BN/niC+DLL2Va//PP690b8mFBQVq5vi0mk+VVb+oIW22tR+OnTskfq5oaee7p0xKHDnW8v126SEIUFtY8QkMlQkIsj0NC5Hlqax7BwZZhNMofPF+eM6UokqTU1sq/nXlUV2tRVWV5XFkpYX5cWSnz3tSorNQSn7bWummP0FBJsK0rkjExltVL8yomLybwPEyE7LR4MfCHPwCjRrnp5YM1NcCcOXI8d66sZEXkAfz8tD8uffva/7yaGm0Ef/q05cjevDWvBJgfV1TIH2ZA+8NbXOz496cyGCQhMo/AQEkag4K048BASZoCAiyPAwKkcqWGetvPT763n58W6h9ig8HyWL1GWFGah8lkGY2NWjQ0aMf19XK7oUE7rq+XKqB5W1srx7W12rErr1E2GiW5ta4Gqse2KofR0Vp1MSqK89Z8BS+fb4N6+R1QBiACYWGyifukSRKDBrlJ9r94MfDAA3JCOTubywwT2aG21vI0inmFwbziYKsyYat6UV1tWelQEy1qzmi0rJiZV9bMq23m1Ti1Na/WmVfvzE93uuWAlVyKe405iPqDvPzyMvzwQwROnrT8enw8cN55khSdd54sPOXyxOj4cdm0paoKWL4cuPFGF3eAiGxpbJSEyLo6ooatSkpdne2Ki3VlRg21mqO2jY3y2mqlx/zYukKkhnU1yc/PsvpkHoGBWqVKba0rWmprXQELCtISH05yJ2djIuQg5j/IsLAI7NgBfPcdsGYN8OOPknuYS08HJk6UOO88++ZIdNoNNwD/93/A2WdLp9yiREVERKQfJkIO0toPsq4O2LRJkqLvvwd++aV5Kbx3by0xGj9ezlw51A8/yDc2GICtW4Hhwx38AkRERJ6HiZCDtGeLjcpK2TX8+++BtWuBLVuaL5jVt6/MMZowwQGJUUODbKq6cydw553Aa6914psRERF5DyZCDtKZvcbKyuRM1fffA+vXy2bw1j/t3r0lIVIjLa0dL/Dqq8Bdd8klDgcOyMpzRERExETIURy56WppqSRG69ZJxWj79uaJUVqaTPUZN05iyJAWFtw6eVIukT99GnjlFeBPf+pU34iIiLwJEyEHcebu86WlwE8/yTSf9etlio96xYcqNBQYPVqSorFjgTFjZL0VzJoFvP667IewdSuXxiUiIjLDRMhBnJkIWTtzRiZfb9ggsXGjnF6zltG9BmMP/x/GYgPGLr0D/W8ewTyIiIjIDBMhB3FlImTNZAL27LFMjPbvb/648HBg5EipFo0ZIxWkrl1d2lUiIiK3wkTIQfRMhGw5+fqH+GXWMmwM+B02jv4Lft0RjDNnmj+uRw/ZDmT0aGnPOktWaiUiIvIFTIQcxK0SoYoKWUG6oAB44glg4UI0NkrV6JdftNizp/lTAwKAwYMlKRo5UtoBAzi1iIiIvBMTIQdxq0RowQLgqaeAXr2ArCxZp96GsjJZw2jTJi2Kipo/LiREliEaORIYMULaXr24MDUREXk+JkIO4jaJ0IEDwMCBsnT1qlXAH/5g91MVBTh2DPj1V4nNmyVRsnVKLSpKS44yMyW6d2dyREREnoWJkIO4TSJ00UXAl18CF1wArF7d6cyksVE2qf/1V0mKtmyRdY1qa5s/NiZG5hipiVFmpsxBYnJERETuiomQg7hFIrR6tVSAAgOB3btlnw4nqKuTM25qxWjrVmDXrub7pwFAZKQkR8OHy1JGQ4cC/fvL7tJERER6YyLkILonQrW1wKBBQE4OMH++zBFy8cvv3i1J0datwLZtsrVZXV3zxwYESDI0ZIgWgwfLfmqsHhERkSsxEXIQ3ROhJ58EFi4EkpLkXFZ4uOv7YKW+Xq5M27ZNYscOSY5sLf4IyFZoalKkxsCBgN5zz4mIyHsxEXIQXROhvDy5XL6yEli+HLjxRte+fjuoE7J37pTYsUNOq+3f33zbEFVamhS71Bg4EMjIkKvZiIiIOoOJkIPomgjdeCPw3nuyC+uPP3rk+aWaGmDvXkmK1Ni9W3I8WwwGoGdPSYoGDNBaJkhERNQeTIQcRLdE6Mcfgd/9TjKDrVtlVrIXOX1aJmbv3i3JUVaWxIkTth9vMMhl/P37S2LUv78kR/37y6k3IiIic0yEHMSliVBjoyRAeXnAokVAbi5wxx2yy7yPKC7WkqKsLJmLlJUFnDzZ8nMSErTEKCNDziZmZMipNz8/1/WdiIjch71/vwNc2KcOO3z4MB599FF8//33KCwsRHJyMm666SY8+OCDCGrleu2amhrMmzcPK1asQG1tLaZMmYJXX30VCQkJLuy9nT75BPjLX4Djx7X7DAbZRdWHdO0qMXGi5f0lJZIU7d2rtXv3Ss5YVCSxbp3lc7p0Afr0kcSob1/LNirKVe+IiIjcmUckQvv27YPJZMIbb7yB3r17Y/fu3Zg5cyYqKyuxZMmSFp93zz33YPXq1fjwww8RGRmJu+++G1dccQV+/vlnF/beDp98Alx1lcw4NqcowK23yuVVV1yhT9/cRHw8MH68hLmKCmDfPkmKsrPlODtbFuKurtYmb9v6fn36SPTtqx337g2EhbnmPRERUeedPi2f+Wrs3y9tgJ0ZjseeGnvmmWfw2muv4eDBgza/XlZWhvj4eLz33nu46qqrAEhC1b9/f2zcuBFj7Ky0OP3UWGOjTH4xrwSZMxiAlBTg0CHukNoODQ3A4cOSFGVnyy+G2ubnt/7cxEQtKVKjVy8JVpKIiFxLUWT+aG6uLKlnHgcOAKdO2X6e0ViO2lovOTVmS1lZGWJiYlr8+tatW1FfX4/Jkyc33ZeRkYG0tLRWE6Ha2lrUmu0zUV5e7rhO2/Ljjy0nQYB2XfqPPwITJji3L14kIEBLYi66yPJrFRWWowfzEcTJk0BhocSPPzb/vtHRsr2IeXTvrgWvbCMiar+yMhm8Hj4s4361PXQIOHhQVpFpTVJS8wp/UhIwdmzbr+2RiVBOTg5eeumlVk+LFRYWIigoCFFWQ/iEhAQUFha2+LzFixfjkUcecVRX21ZQ4NjHUZvCw2V7kLPOav6106e1UYeaJOXmShQVyddPn5aFJG3p2hVIT5ekKD3d8jgtTbYmISLyJYoig8yjR4EjRyTJMW+PHJHP1daoJ0d69dIGuWrlvlcvIDS0+XPsrWPomggtWLAAT7WxZcTevXuRkZHRdDsvLw9Tp07F1VdfjZkzZzq8TwsXLsTcuXObbpeXlyM1NdXhr9MkKcmxj6NOiY4GRoyQsHbmjDZKOXjQcvRy6JD80hUXS2zebPv7R0RIQmQeqalapKRwvzYi8izV1XLi4uhRadVQE5+jR+UxbYmLa15l79lTIj0dMBqd039dE6F58+ZhxowZrT6mZ8+eTcf5+fmYOHEixo0bh3/+85+tPi8xMRF1dXUoLS21qAoVFRUhMTGxxecZjUYYnfXTtuXcc+WvX15e88nSgJYGn3uu6/pENoWFaatg21JaKgmROsJRRzyHD8sHwcmTkizt3i1hi8EgywGkpFhGt25a260bT8ERkfMpinxm5eVpcfx482hteRNziYnNK+Xmt/W6UEXXRCg+Ph7x8fF2PTYvLw8TJ05EZmYmli5dCr82FojJzMxEYGAg1qxZgyuvvBIAkJ2djaNHj2KsPScNXcXfH3jhBblqzGCwTIbUlaSff54TpT1AVJSse9nS2peVlTJKUkdI6ujJfBRVW6vNUdqypfXXUpOi5OTmkZQkHzqsLhGRLdXVMuOioEAuILEONfE5c8a+7xcWZlndTk3VpgSkp8tAzpU1hvbwiKvG8vLyMGHCBKSnp+Ott96Cv1lSoFZ38vLyMGnSJLz99tsYNWoUAGDWrFn48ssvsWzZMkRERGD27NkAgA0bNtj92i5bUNHWOkKpqZIE+fil875CvTLi+HFJiqxHXeporKrK/u8ZGytJkRqJic0jIUFOCXrgDi5EZKaxUaozRUXagMo81MSnoKDlTbJtiYzUBl7qKXzriIpyv88Qr1pQ8dtvv0VOTg5ycnKQkpJi8TU1j6uvr0d2djaqzP5KPPfcc/Dz88OVV15psaCiW7riCuDSS+VSpYIC+at17rmsBPkQg0HWN4qPb7mqpCjyAaaO1myN5PLz5UOvvl4+FE+ebPlUnCogQCZ6JyRo0bWr9EVd5FI9jovjqTkiV1AUqciUlEgUF2utGuqCsurXTCb7v39wsPypsVVVVhOfbt1sT0T2Jh5REdKTrpuuEnWQySRra5iPAAsKbI8US0vb//1DQrSkLT5ekqPY2OZtbCwQEyNtly4Of5tEHkNR5PT4yZPyu6kOUk6csGxLSuRYTX7MVnOxi8Egv2+2Kr/m1eGkJKn0uFsVx5G8qiJERO3j5yfJSFwcMHhw64+trbUcWaphPgpVo6REKk1VVdqEcHt16SJJkRrR0VqrRlRU8zYyUkau3vyBTZ5BUeT/fmmpFqdPa615nDqltWrU1XXsdYODm1dm1WPzKm5Cgtxn74rKJPjjIvJxRqM2ubEtiiILUqpJkjpyVUe0aqi31ZFvY6NMzlRP6bVXUJAkRJGRkhxFREhERsq6UBER0oaHy6RN6zYsTMr7YWGSkDGp8h0mkyQvZ85IRebMGYmKiuZtRYVcJWUeZWValJbK/+XOCArSKqXqYEWtoqrH5pXW+HjvPzWlNyZCRGQ3g0FLQnr1su856iW4alJkPVpWR9C2RtdlZfL8ujot+XLEewgNldN7oaGWxyEhEl26WB536SKjcus2OFgSSbW1jqAgrfX39+0ETFFk65u6OqlC1tZaHtfWAjU1zdvqagnz4+pqSW7UVo3KStuto/n7265eRkXZrnaqp4djYuT/mS//P3BHTITsNHeuzF0ePVqW8G7j6n0i+h+DQavm9OjRvueaTDJaV0fj6sjcfLReUSGt+aje/FitAqh/ENUJqPZeFuwoBgMQGChJkdoGBMixdevvL8fmrRp+fpatwSDh52fZqq9p3qrvX22tw2TSWpNJqh/WbUND87ahQU6ZWrd1dZatntQEWK0MWlcQ1VCri5GRWtKvnqJVK5IhIUxmvAknS7dBnWwFlAGQyVZRUcDIkZIUjRolkZCgZy+JqC3mp0jUxEitGqhhq9LQUkWipQqGeZWDWmYwWFbObFXYrKtw6nFLlTtbFT711ChPifoeeydLMxFqg/qDvPvuMmzfHoEtW+TDzlp6upYUjRwp+1iFh7u+v0TkHtRTQeopIOsKSV1dy5WUxkbb1Rfr6kxjo2U1Rw319a1bW5Ui62qSemyr+uTnJxUq62qVrapWQIBl9cv82GjkhF5yPiZCDmL9g6yvB3btAjZtAn79VWLv3ua7YxgMQP/+khSpMWSIjGaIiIjIuZgIOYg9P8jycmDrVkmONm+WOHas+eMCAuRS5pEjZVPPzEzZt4rbIBARETkWEyEH6eiCioWFWlK0ebPsG3XiRPPHBQVJpSgzUwsmR0RERJ3DRMhBHLWytKLI5ppbtkhs3ixVJFur+gYGSuXorLO0GDKEK/MSERHZi4mQgzhziw1FAQ4dkoTIPE6fbv5Yf38gI0Pb3Xz4cGDYMFmjgoiIiCwxEXIQV+81piiybcG2bVps3SrbG9iSlibVIvPo04dXZBARkW9jIuQg7rDpqqLIjuK//WYZhw/bfrzRKFesDR5sGcnJXEeDiIh8AxMhB3GHRKglpaVyKf/OnVrs2iULw9kSHS0Tsa0jJsal3SYiInI6JkIO4s6JkC0mk8w72rXLMvbv1xZas5aYCAwc2DyiolzadSIiIodhIuQgnpYItaSmBti3D9i92zKOHGn5OcnJwIABWgwcKKfcYmNd128iIqKOYCLkIN6SCLWkogLYswfIyrKM48dbfk58vCRE1pGSwjlIRETkHpgIOYi3J0ItKSuTCpKaJO3ZI9FaBSk0FOjXTy7zz8iQ4379gL59uQYSERG5FhMhB/HVRKgllZWSIO3daxk5ObIxpC0Gg1zmryZGanLUty+QmiobORIRETkSEyEHYSJkn/p6maS9d6+WKGVnS9haIFIVHCzrHvXtK635cdeuPNVGREQdw0TIQZgIdY6iyB5r+/ZpidH+/RK5uZJAtSQiAujdW6JnT6BXLy26dZPVtomIiGxhIuQgTIScp6FB5hypydGBA1ocOSJJVEsCA4Hu3SVB6tFDa9WIjmY1iYjIlzERchAmQvqoqQEOHpS5Rzk5cpybK3H4cOuVJECqSd27a4lR9+6WERnp7HdARER6YiLkIEyE3E9jI5CXJ8nRwYMyNyk3V9rDh4HCwra/R2QkkJ7ePNLSJBISOImbiMidNTQABQXA0aNyFsE6goPL8dtvTIQ6jYmQ56mqkl+CQ4ckjhyRBEmNkpK2v0dgoFzRpiZGqanabfWYVSUiIudQFODkSeDYMS2OHrU8zsuTgXFLunQpR3U1E6FOYyLkfSorbY8gDh+WX7C8vJa3IzEXHi6LSKakSGKkHnfrpkVsLOcqERGZM5mA4mL5rD1+XGuto7q67e+lDlpTU5tX+GNjy3HWWUyEOo2JkO9paADy87UEyXxEoo5EWlsSwJzRqCVFyclaqx4nJclxaKhz3xMRkbMpClBeLp+fBQWS4OTna635cUvrzlnr2rV5NV6t1Kentz6NgXOEHISJENlSWWl7BKNWlPLy7DsFpwoPl4QoKUmLxETL48REICaGFSYicq3GRlkGpbBQoqBAa80jP9++Kg4gn2OJiVoV3VZ1PTlZ1prrKCZCDsJEiDqqtlY+GI4fbz4aMj+uqrL/ewYGyggoIUE+RNTjrl0tj7t2ldNyXGuJiGypr5fkprgYKCqSUI+LiyXRKSqStrjYvukCqshIGcC1VAnv1k0+vwIDnff+APv/fgc4txtEvsto1C7fb4miyMa35iMq69GWenz6tHx4qdWnthgMQFycJEXx8VobFyetGnFxkjTFxkqficjzVFXJ5OKTJyXBKSmxHcXFEvae3lepnye2qtXqKX71vpAQ57xHZ2EiRKQjg0HWPIqIkD3YWlNb23ykZmskV1QkH4aKon342Ss0VEuMYmIkzI+jo5u30dGyqS5P2RF1jqLIafdTpyRRUVv12DxOntTaEydk7bX28vOT33frynLXrtrpeLX6HB8PBHhpxuClb4vI+xiN2mTBtjQ0aGVv81Gg+chQHTWeOCEfqCaTfAhXVsok8fYICgKioiQpiopqHpGRWmsdEREyR4qn8cjTNTTIZOGyMgnz49LS5m1pqSQ56nFpqf2TiG0JCJCBi62qr1oVNo+YGK6XBjARIvJKAQHaiM4eJpN8OJuX1q1HoSdPWo5S1baxEair05KtjgoLk4RIrZCFh7ccYWHNIzRUa0NDJTkjaomiSJVVTf4rK4EzZ2xHRYXtKC/X2vJy+ycKtyUoqHnVtaUKrfmp7fBwVmY7gokQEcHPT/vA7d3b/uepc5ysR7dqa2skbD1arq2V76X+0SkocMx7CgjQkqKQEC1CQ+VUXkiItNbHwcHNW6OxeWseQUHaMStb7aMokkzX1krU1WnHatTUWLbV1XJs3VZVyXF1tXZcVaVFZaXWVla2bwJwe3Tp0rzqaasyqlZQrduQECY0rsREyE6LFwOjRwPDh8v6BfxPSmQ5xyktrWPfo7ZWEiLzUbYaLY3ErUfv5veppxYaGrSky5X8/ORqmKAgicDAliMgoHn4+2utdfj5SajHBoPWqqHeBpq3gLaZsaLYDpNJa62jsVGioUE7Vm+bR2OjTOw3j4YG7biuTov6+tY3WHaFoCCtomhdcQwNbbkyqf7fN69iRkQ4/2oocixePt8G9fI7oAyAXH4XFQUMGyYxdKi0AwawFE/kDurqLE93mFcEzKsCtioHNTW2Kw3WVYmaGsvKBTmOwWBZaQsObl6Ns67YqcfW1b0uXSwrgtbHanjrJGBfx3WEHET9Qd5wQxmysiKQlWV7MltgINC/vyRG5hEf7/o+E5HrKIp8JqhJkXnFo75eu8+8ImJeJbEV5tUWNcyrMubH1tUc89M95p/uimJZGTKvFplXksxb8yqUeTXKOlqqbllXv6wrZebH5qcWWXEnR/CqROjw4cN49NFH8f3336OwsBDJycm46aab8OCDDyKolTLMhAkTsH79eov77rjjDrz++ut2v7b1D7K2FtizB9i+HdixQ9rt21suvycmSkI0ZIgWGRmsHhERETmTVy2ouG/fPphMJrzxxhvo3bs3du/ejZkzZ6KyshJLlixp9bkzZ87E3//+96bbIZ1c6clolHlCw4dr9ymK7D+lJkc7d0qbm6stSf7119rjAwIkGRoyBBg8GBg0SFrOPSIiInItj6gI2fLMM8/gtddew8GDB1t8zIQJEzBs2DA8//zzdn/f2tpa1Jqd9C8vL0dqamqHttg4cwbYvVuSol27JEHaubPl6lFEhCRFAwdKDBggkZzMBImIiKg9vKoiZEtZWRliYmLafNy7776L5cuXIzExERdffDH++te/tloVWrx4MR555BGH9DEsDBgzRkKlKLIxp5oY7dolsW+fXCWzYYOEuchISYj695dQj9PTuRgWERFRZ3hkRSgnJweZmZlYsmQJZs6c2eLj/vnPfyI9PR3JycnYuXMn7r//fowaNQqffPJJi89xZEWoPerqgP37JSnaswfIypI2J0cmRNrSpYtsy9C/v5xqUxOlPn24ZxQREfk2j5gsvWDBAjz11FOtPmbv3r3IyMhoup2Xl4fx48djwoQJ+Pe//92u1/v+++8xadIk5OTkoFevXnY9R+/d52trgQMHJDHau1dizx5JmurqbD/Hz082+szIkEQpI0M7jo/naTYiIvJ+HpEIlZSU4OTJk60+pmfPnk1XhuXn52PChAkYM2YMli1bBr92nheqrKxEWFgYvvrqK0yZMsWu5+idCLWkoQE4eFBOqe3dq7V798optpZERUlCZB59+8pqwl26uKz7RERETuURc4Ti4+MRb+dCO3l5eZg4cSIyMzOxdOnSdidBALB9+3YAQFJSUruf624CAiSB6dsXuOQS7X5FkavUsrMlOdq3Tzs+ckS2Odi0ScKcwSCbearfs08fre3enSulEhGRd/KIOUJ5eXmYMGEC0tPT8dZbb8HfbDOfxP/tKpmXl4dJkybh7bffxqhRo5Cbm4v33nsPF154IWJjY7Fz507cc889SElJaba2UGvctSLUEdXVMucoO9sy9u+XBKkl/v5yqq1PH4nevbU2PZ1JEhERuR+PqAjZ69tvv0VOTg5ycnKQkpJi8TU1j6uvr0d2djaqqqoAAEFBQfjuu+/w/PPPo7KyEqmpqbjyyivx0EMPubz/7qJLF1mvaPBgy/sVRXYW379fi+xsmZuUk6MlUDk5wH//a/ncgABJhnr3Bnr1klCPe/bk6TYiInJvHlER0pM3VYQ6wmQC8vMlKVITo5wcOc7NlSSpNcnJWlJk3vboAXTtyonbRETkHB4xWdoT+Hoi1BqTCSgo0JKi3FxJktS2tUnbgGx82LOnRI8eMhepRw+J9HRZP4mIiKgjmAg5CBOhjlEU4NQpSYoOHrRsDx2SRSXb+p8XFSUJUVqatOaRliYVJS4oSUREtnjVHCHyPAYDEBsrMWpU86/X1clVbIcOacnR4cNae+KETOAuLZUtSmwJCpIr3dLSJFJTtVBvM3clIqLWMBEiXQQFaVeh2XLmjCRKahw9anm7oECSKfWUXEsiIoCUFEmKUlIsj7t1kzYyknOViIi8gaLIQDovDygutu85PDXWBp4ac0/19TKJ++hRLUk6dswyTp+273uFhGhJUbduMsG7WzctkpOBpCQuE0BEpKfqahkE5+XJ539eXvPIz5cdGQAgJaUcx4/z1Bh5qcBAbb5QS86cAY4flzh2zPI4L0+OT50Cqqq0q+JaEx8vSZEaSUnNIzGR+7wREbVHVZUkOLYiP18Lewe3gMwhTUiQz/m2sCLUBlaEvFtVlfyCqUmSOsowH20UFEgFyl4xMZIQqZGUJL+QiYnSqsdxcbJYJRGRt6mvl1NThYVAUZGEelxYKJ+rhYUSbV1hbC442LJab13FT0mRz1yjkZOliewSEiILQPbu3fJjTCapHJmPTNQESf1lVo/r6uSxp07J5rit8fOTZEgduZi35hEfL21oKOcyEZE+FAUoKwNKSiTBKS7WjouKmrenTrXv+4eENK+uJyVpiY4azpjTyYpQG1gRInspipRurUc7BQWWo6GiIvkAae9vXnCwJEXWERdnO2JiZOVvIiJrdXWyo8CJE82jpKR5nDjRvso4IBXvrl2bV8PVRMf8ODzc8QkOK0JELmYwSPIREwMMGND6Yxsa5INFHT1Zj6jMR13FxTJJsKZGmwhur8hIbRkD84iJ0Vo1oqOljYriKTsiT1FfLwOwU6e0Vo2TJ7XWOs6c6djrhYdbVqvj47Ukx7q6HRPjGWu9MREi0kFAgDYiskdlpe1RWkmJfKipIzZ1NFdaqpWyy8pkMcv2iIyUxCgqSlo1oqLka5GR2nFUlCxToN4fEcEr7IjsVVsrv6Pl5drva1mZ/A6bH5eWSqKjtmp0NKEBZMATEyMVZPPqcmys7epzfLxUpr0NEyEiDxAaKtG9u32Pb2yUD0m19K2OAm2NEs1HkeqHqvoB3FFdukhCZB7h4VprHup9YWFaqLdDQ2XugCeMKsk3NDbKRRZnzkhUVFgetxTl5Vqot8vK5BSVI0RGWlZ3bVV/Y2O1RCc2Vp7D3y0mQkReyd9fG93162f/8+rqZMSpltnVKCvTWuuRqvkotqpKvk91tURRkWPeT0iIlhiZJ0hqgqjeto4uXSTMj80jONgyOBndc5lMcvq4pkY7laweV1Vp/yfVqKrSQr1dWamF9e0zZ6Rta6PpjlIHBdbVVvMKbHS0Vq1VIyZG7uN8wI7jj85OhYXOmcxF5E6CgrTz/x3R0GBZ4m9tNGw9Yq6stBxdm5f81T9YzhYUJAmR0ai15hEUZHlsHYGBWquGejsgQAvz2/7+zVs1/Pwsj63DYNBaNdTbKlufWepEfUVpHiaT5bF5NDZKWB83NMixeWse9fWWx3V10ppHXZ3tqK2VMD9WQ012amvbP5G3s/z8LKuY5tVM62qnemxdIVVPJYeHc16enpgI2alfP8m8Bw7UYsAAabt2ZYJEBMgfcrU831kmk4y+1ZG4eWs9WldH6uajfPPRvnUloLpa/nhWV8vrqNQ/vuTZAgK0Kp+tSmCXLs2riGrl0LrKaF6FNG9ZQfQevHy+DerldwZDGRTF9uV3aoI0YIBE//7SJifzF4XInSmKVCnUUyhqlcG6VasR1hUKtbJhXr2wVeloqTJiq4qiVlqsw1aFxrx6Y17NUd+bdat+Hpm3LYWtCpR5hcq8UtVSdcu6EqbeZ101CwzUqmzq19WwrsapVTtblTv1dCdPExFg/+XzTITaoP4gi4rKkJ8fgawsNMWePbLhZ0s/wYgISYqso0cPlkGJiIiciYmQg7T1g6yuBrKzJSlSk6O9e4GcHBnF2WI0An37SlKUkaFF375SdiUiIqLOYSLkIB1dWbq2VpKhPXsk9u2TBCk7W0rtLUlNlaSoXz/LSEnhZY5ERET2YiLkII7eYqOxEThyxDIx2rdPoqSk5eeFhAB9+kjVqF8/afv2lfscMTGViIjImzARchBX7jV28qQkRNnZWuzbJ/OQGhpafl5MjLZxaO/ekhz16iXHcXGcsE1ERL6HiZCDuMOmq/X1wKFDwP79khyp7YEDshN6a8LDJSHq1csyevaU03CctE1ERN6IiZCDuEMi1JrKStlH6sABmZOUkyPHubnA8eOt73AeGChbNvTsKaEmSD17ypVtbvh2iYiI7MLd531EaCgweLCEtZoaqSTl5kqClJurxaFDUmk6cEDClthYSYhsRVqad26+R0REvoUVoTa4e0Wooxobgbw8SYoOHpTE6OBBLVqbuK1KSpKkqHt3LdLTpWWiREREeuKpMQfx1kSoLRUVkhypoSZLhw9LW1nZ9vdITJTESI20NMvjyEhO5CYiIudgIuQgvpoItUZR5Ao388ToyBE5Vlt7EqXwcC05Sk2VY/M2JUWW0yciImovJkIOwkSo/dRE6cgR23H0qHzdHgkJkhSpkZKitSkpsp8bkyUiIrLGRMhBmAg5R2UlcOyYJEVHjsixeltta2vt+15du0pS1K2bFua3k5N5Go6IyNfwqjFya6Gh2h5rtigKcOKEJEXHj2uJkno7L0/a2lqguFhi27aWXy8kRBKi5GSZ5J2cLHOYkpK0NilJFqdkwkRE5DkaG+XvRUGBRGGhtHV19j2fFaE2sCLkvtRTcMePa8mReaj3lZba/z0DA+V0XGKiFurthATLYJWJiMg5TCbg9GlJaoqKLKOw0DKKi+Xx1uLjy1FSwlNjncZEyPNVVcnoIC9Pa9URg3lr77wlldEop+W6dtWSI/W2GvHxWsu5TETky6qrJWkpKdEq+eqxmuSoxyUlrW8tZc1gkM9a80p/XFw5lixhItRpTIR8h3qazXykUVDQfCRSVCTLC7RXRIQkRNYRF6eFejs2lhUnInJfasXmxAnLKCnRWuuoqmr/60RHawNN8wq9dcTHAwFWk304R4ionYxG7eq0tlRVaSMadRRjPpJRb6sjnsZGoLxcIjfXvv4EBMicJTUxso6YGMtjNbiQJRHZS1Hk8+zUKS1OnpQwPzaPEyckCbJ1OqotQUGW1XL12LqqnpAg9xuNjn/P1pgIEXVASIi2mnZbTCaZp2RrhGRrFHXypFxV19CgJVPt0aWLjKKioyUxUo/NIyrK8liNkBBWoYg8jaJIlbq0FCgrkyTl9Gm5bX586pR2+/Rp7ba9k4ptiYhoXtE2v20dERHu9xnDRIjIyfz8tGpNv372PaemRht5mbe2RmmnT2v3m0xyHr66GsjPb39fAwLklFxUlLQtRUSEhPlxeLjWWpeoici2ujpJYsrLtbasTKsgq8dlZZahJj1qdKQ6Yy4wUKsyR0e3XH1WK9RxcXK/N8x99JiPq0suuQTbt29HcXExoqOjMXnyZDz11FNITk5u8Tk1NTWYN28eVqxYgdraWkyZMgWvvvoqEhISXNhzovYLDtbWQbKXySQfpOooz9boTx0hWo8Uy8qkAtXQoCVYndGliyRELUVYmBbq7dDQ5q0aISHyQU2kF0WRpKWqSiq2apw507ytqJBWjYqKlsPe9dLsERSkVXdtVX5bqhLHxsrvmbtValzFYyZLP/fccxg7diySkpKQl5eHe++9FwCwYcOGFp8za9YsrF69GsuWLUNkZCTuvvtu+Pn54eeff7b7dTlZmnyBOk+gtFQLW6NPW6PVsjLnfKhbCwyUhEhNjGxFly4tR3Cw5bEaRqPWWkdgoO/+cXBnalJSW9s8amok1OPqaq21Pq6ulv/31rfNo7JSaxsbnfeeunTRKqrWVdfw8OZVWvW2+altzg+05PUrS3/++ee47LLLUFtbi0AbQ8WysjLEx8fjvffew1VXXQUA2LdvH/r374+NGzdizJgxdr2O+oPcs6cM/fszESJqTW2tlhSppX51dGx+bD1qrqhoeYTd2ZJ/ZxgMMso2Gi1bNQIDLY/NIyCg+W3r8PeXMD82Dz8/y2M/P+mT+bEa1rfN3wMgfaivl2P1U19RWg+TSQtFkUSgsVFuWx83NGj3qbdtRX29hPVxXZ0cm7fmUVtr2eopIKDlCqZ5xdP6WL2tHpufVubpZMfz6qvGTp06hXfffRfjxo2zmQQBwNatW1FfX4/Jkyc33ZeRkYG0tLRWE6Ha2lrUmg1ry8rKAAA5OeXtOk1B5KuCgrT5BJ2ljvwrK7XRemWljOrVkbw6cm9p5K9WCKqr5Y+oep/6B9W8elBba5l4KYpWafB0Y8cCGzfq3Qvn8Pe3rOyZV/jMq39qmFcIzVu1qhgaKm1IiNyvViHVrzn6NG1HLiuntpWXlwMA2qr3eFQidP/99+Pll19GVVUVxowZgy+++KLFxxYWFiIoKAhRUVEW9yckJKCwsLDF5y1evBiPPPJIs/svucSOa6qJiNyUtyZBgFSg1ISYyFpFRQUiIyNb/Lqup8YWLFiAp556qtXH7N27Fxn/25DqxIkTOHXqFI4cOYJHHnkEkZGR+OKLL2CwcRL/vffewy233GJR3QGAUaNGYeLEiS2+rnVFyGQy4dSpU4iNjbX5Oo5WXl6O1NRUHDt2zOvmJHnzewP4/jydN78/b35vAN+fp3PW+1MUBRUVFUhOToafn1+Lj9O1IjRv3jzMmDGj1cf07Nmz6TguLg5xcXHo27cv+vfvj9TUVPzyyy8YO3Zss+clJiairq4OpaWlFlWhoqIiJCYmtvh6RqMRRqsVnKyrSq4QERHhlf/hAe9+bwDfn6fz5vfnze8N4PvzdM54f61VglS6JkLx8fGIj4/v0HNN/zuRb13xUWVmZiIwMBBr1qzBlVdeCQDIzs7G0aNHbSZORERE5Hs8Yo7Qpk2bsHnzZpxzzjmIjo5Gbm4u/vrXv6JXr15NSU1eXh4mTZqEt99+G6NGjUJkZCRuu+02zJ07FzExMYiIiMDs2bMxduxYu68YIyIiIu/mEYlQSEgIPvnkEyxatAiVlZVISkrC1KlT8dBDDzWdxqqvr0d2djaqzGbLPffcc/Dz88OVV15psaCiOzMajVi0aFGz03PewJvfG8D35+m8+f1583sD+P48nd7vz2PXESIiIiLqrJanURMRERF5OSZCRERE5LOYCBEREZHPYiJEREREPouJkBvr3r07DAaDRTz55JN6d8vhamtrMWzYMBgMBmzfvl3v7jjMJZdcgrS0NAQHByMpKQk333wz8vPz9e5Wpx0+fBi33XYbevTogS5duqBXr15YtGgR6vTeCdOBHn/8cYwbNw4hISG6LKjqaK+88gq6d++O4OBgjB49Gr/++qveXXKIH374ARdffDGSk5NhMBjw2Wef6d0lh1q8eDFGjhyJ8PBwdO3aFZdddhmys7P17pZDvPbaaxgyZEjTIopjx47Ff//7X136wkTIzf39739HQUFBU8yePVvvLjnc/PnzkZycrHc3HG7ixIn44IMPkJ2djY8//hi5ubm46qqr9O5Wp+3btw8mkwlvvPEGsrKy8Nxzz+H111/HAw88oHfXHKaurg5XX301Zs2apXdXOu3999/H3LlzsWjRImzbtg1Dhw7FlClTUFxcrHfXOq2yshJDhw7FK6+8ondXnGL9+vW466678Msvv+Dbb79FfX09zj//fFRWVurdtU5LSUnBk08+ia1bt2LLli0477zzcOmllyIrK8v1nVHIbaWnpyvPPfec3t1wqi+//FLJyMhQsrKyFADKb7/9pneXnGblypWKwWBQ6urq9O6Kwz399NNKjx499O6Gwy1dulSJjIzUuxudMmrUKOWuu+5qut3Y2KgkJycrixcv1rFXjgdA+fTTT/XuhlMVFxcrAJT169fr3RWniI6OVv7973+7/HVZEXJzTz75JGJjYzF8+HA888wzaGho0LtLDlNUVISZM2finXfeQUhIiN7dcapTp07h3Xffxbhx4xAYGKh3dxyurKwMMTExeneDrNTV1WHr1q2YPHly031+fn6YPHkyNnrzdvReqqysDAC87netsbERK1asQGVlpS5bYDERcmN//vOfsWLFCqxduxZ33HEHnnjiCcyfP1/vbjmEoiiYMWMG7rzzTowYMULv7jjN/fffj9DQUMTGxuLo0aNYuXKl3l1yuJycHLz00ku444479O4KWTlx4gQaGxuRkJBgcX9CQgIKCwt16hV1hMlkwpw5c3D22Wdj0KBBenfHIXbt2oWwsDAYjUbceeed+PTTTzFgwACX94OJkIstWLCg2QRo69i3bx8AYO7cuZgwYQKGDBmCO++8E88++yxeeumlFjeadQf2vr+XXnoJFRUVWLhwod5dbpf2/PsBwH333YfffvsN33zzDfz9/TFt2jQobrqYe3vfGyB7/E2dOhVXX301Zs6cqVPP7dOR90fkLu666y7s3r0bK1as0LsrDtOvXz9s374dmzZtwqxZszB9+nTs2bPH5f3gFhsuVlJSgpMnT7b6mJ49eyIoKKjZ/VlZWRg0aBD27duHfv36OauLnWLv+7vmmmuwatUqGAyGpvsbGxvh7++PG2+8EW+99Zazu9ohnfn3O378OFJTU7FhwwZdyr9tae97y8/Px4QJEzBmzBgsW7YMfn7uPa7qyL/dsmXLMGfOHJSWljq5d85RV1eHkJAQfPTRR7jsssua7p8+fTpKS0u9qkJpMBjw6aefWrxPb3H33Xdj5cqV+OGHH9CjRw+9u+M0kydPRq9evfDGG2+49HU9YtNVbxIfH4/4+PgOPXf79u3w8/ND165dHdwrx7H3/b344ot47LHHmm7n5+djypQpeP/99zF69GhndrFTOvPvZzKZAMBtK3rteW95eXmYOHEiMjMzsXTpUrdPgoDO/dt5qqCgIGRmZmLNmjVNCYLJZMKaNWtw991369s5apOiKJg9ezY+/fRTrFu3zquTIED+b+rx+chEyE1t3LgRmzZtwsSJExEeHo6NGzfinnvuwU033YTo6Gi9u9dpaWlpFrfDwsIAAL169UJKSooeXXKoTZs2YfPmzTjnnHMQHR2N3Nxc/PWvf0WvXr3cshrUHnl5eZgwYQLS09OxZMkSlJSUNH0tMTFRx545ztGjR3Hq1CkcPXoUjY2NTetb9e7du+n/qqeYO3cupk+fjhEjRmDUqFF4/vnnUVlZiVtuuUXvrnXamTNnkJOT03T70KFD2L59O2JiYpp9xniiu+66C++99x5WrlyJ8PDwpnldkZGR6NKli86965yFCxfiggsuQFpaGioqKvDee+9h3bp1+Prrr13fGZdfp0Z22bp1qzJ69GglMjJSCQ4OVvr376888cQTSk1Njd5dc4pDhw551eXzO3fuVCZOnKjExMQoRqNR6d69u3LnnXcqx48f17trnbZ06VIFgM3wFtOnT7f5/tauXat31zrkpZdeUtLS0pSgoCBl1KhRyi+//KJ3lxxi7dq1Nv+dpk+frnfXHKKl37OlS5fq3bVOu/XWW5X09HQlKChIiY+PVyZNmqR88803uvSFc4SIiIjIZ7n/iX0iIiIiJ2EiRERERD6LiRARERH5LCZCRERE5LOYCBEREZHPYiJEREREPouJEBEREfksJkJERETks5gIERERkc9iIkREPq2goAA33HAD+vbtCz8/P8yZM0fvLhGRCzERIiKfVltbi/j4eDz00EMYOnSo3t0hIhdjIkREXq2kpASJiYl44oknmu7bsGEDgoKCsGbNGnTv3h0vvPACpk2bhsjISB17SkR6CNC7A0REzhQfH48333wTl112Gc4//3z069cPN998M+6++25MmjRJ7+4Rkc6YCBGR17vwwgsxc+ZM3HjjjRgxYgRCQ0OxePFivbtFRG6Ap8aIyCcsWbIEDQ0N+PDDD/Huu+/CaDTq3SUicgNMhIjIJ+Tm5iI/Px8mkwmHDx/WuztE5CZ4aoyIvF5dXR1uuukmXHvttejXrx/++Mc/YteuXejataveXSMinTERIiKv9+CDD6KsrAwvvvgiwsLC8OWXX+LWW2/FF198AQDYvn07AODMmTMoKSnB9u3bERQUhAEDBujYayJyBYOiKIrenSAicpZ169bh97//PdauXYtzzjkHAHD48GEMHToUTz75JGbNmgWDwdDseenp6TyFRuQDmAgRERGRz+JkaSIiIvJZTISIiIjIZzERIiIiIp/FRIiIiIh8FhMhIiIi8llMhIiIiMhnMREiIiIin8VEiIiIiHwWEyEiIiLyWUyEiIiIyGcxESIiIiKf9f/j1pnVXhQhTwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eta = 2\n",
    "show_trace_2d(f_2d, train_2d(adagrad_2d))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "RtU9tLiml3_2"
   },
   "source": [
    "# RMSProp\n",
    "\n",
    "[Video timestamp](https://youtu.be/UvM0hK4E2dc?t=1206)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "OBbRL5h3l3_3"
   },
   "outputs": [],
   "source": [
    "def rmsprop_2d(x1, x2, s1, s2):\n",
    "    g1, g2, eps = 0.2 * x1, 4 * x2, 1e-6\n",
    "    s1 = gamma * s1 + (1 - gamma) * g1 ** 2\n",
    "    s2 = gamma * s2 + (1 - gamma) * g2 ** 2\n",
    "    x1 -= eta / math.sqrt(s1 + eps) * g1\n",
    "    x2 -= eta / math.sqrt(s2 + eps) * g2\n",
    "    return x1, x2, s1, s2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 301
    },
    "colab_type": "code",
    "id": "nc3_6I-Ul3_9",
    "outputId": "03bdc363-bca6-4a91-eafa-281630282ecc"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 20, x1 -0.010599, x2 0.000000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eta, gamma = 0.4, 0.9\n",
    "show_trace_2d(f_2d, train_2d(rmsprop_2d))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "BD9ILdGVl4AD"
   },
   "source": [
    "# Adam\n",
    "\n",
    "[Video timestamp](https://youtu.be/UvM0hK4E2dc?t=1331)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "vC3McRDZl4AF"
   },
   "outputs": [],
   "source": [
    "def adam_2d(x1, x2, s1, s2 , t):\n",
    "    beta1, beta2, eps = 0.9, 0.99, 1e-6\n",
    "    g1, g2 = 0.2 * x1, 4 * x2\n",
    "    g1, g2 = 0.2 * x1, 4 * x2\n",
    "    s1[0] = beta1 * s1[0] + (1 - beta1) * g1\n",
    "    s2[0] = beta1 * s2[0] + (1 - beta1) * g2\n",
    "    s1[1] = beta2 * s1[1] + (1 - beta2) * g1 ** 2\n",
    "    s2[1] = beta2 * s2[1] + (1 - beta2) * g2 ** 2\n",
    "    m1 = s1[0]/(1-beta1 ** (t+1))\n",
    "    m2 = s2[0]/(1-beta1 ** (t+1))\n",
    "    v1 = s1[1]/(1-beta2 ** (t+1))\n",
    "    v2 = s2[1]/(1-beta2 ** (t+1))\n",
    "    x1 -= eta / (math.sqrt(v1) + eps) * m1\n",
    "    x2 -= eta / (math.sqrt(v2) + eps) * m2\n",
    "    return x1, x2, s1, s2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "rT5IwhY8l4AK"
   },
   "outputs": [],
   "source": [
    "def train_adam_2d(trainer):\n",
    "    \"\"\"Optimize the objective function of 2d variables with Adam-li trainer.\"\"\"\n",
    "    \"\"\"trainer(x1,x2,s_x1,s_x2) should return the updated positions x1, x2 and possible memory terms.\"\"\"\n",
    "    x1, x2 = -5, -2\n",
    "    s_x1, s_x2 = [0,0,0], [0,0,0]\n",
    "    res = [(x1, x2)]\n",
    "    for i in range(20):\n",
    "        x1, x2, s_x1, s_x2 = trainer(x1, x2, s_x1, s_x2, i)\n",
    "        res.append((x1, x2))\n",
    "    print('epoch %d, x1 %f, x2 %f' % (i+1, x1, x2))\n",
    "    return res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 301
    },
    "colab_type": "code",
    "id": "oeQbFML-l4AV",
    "outputId": "f176b4af-3840-41ca-e544-6e19bd596e5d"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 20, x1 0.414218, x2 0.086138\n"
     ]
    },
    {
     "data": {
      "image/png": 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QKSlxfX7ECOCss0TELFgApKRYM05CCCGE+EZEippvf1vqKHV06Mfi40W8nHUWcPbZwKhR3GZNCHGlq0uSZba3e7YdHbqpx52dntbVJeZwuLZOp7lpmqsZUdcom00sKsrcoqPFYmJc+7GxnhYX52l2u1h8vGfL6yQJJiJS1KxYIe2IEcC554qImT+f1asJCQc6OoCGBrHGRrGmJr1tapJgf2Pb0iLW3Kz3W1qA1laxtjZpu7qs/nTBh90u106jJSaKJSW59pOSgORkvVWWkmJuXOYnvSUiRc0jjwAXXQSccAJnGYQEG5om4qKmRuqgqVbZ8eOuVl8vAka17e2BGWdMjO6xUObu4TB6QJRnJCZGN6P3RHlUjK3yvgCuXhnjv5VqlRm9PA6HmNPp6hVSfaP3yOhNcvc4tbe7eqWMHiP1XF2d//+NU1KkUG9amrSDBgHp6a6WkSGWmenaMit7ZBKRouanP2VFa0IChcMhwqSyUjJuV1W59qurxWpq9L5xabivJCR4zvyN3gGj18Ddo5CY6Ol9SEgQEZOQIAImOrr/YwxFNE2ET1ub7sEyerOUh8vo+VKtu5fM6EUzmvKIqcelpb0fZ2qqlKBRlpkpbXa2pN3IytL72dnyXeAkN/SJSFFDCOkfmiZekvJyoKxMWmO/okK36mrxFPSWuDjP2bfZLD0tTZ/Jq1l9crJ4QIj/sdl0T9RATA41TTw/aglReeHq6z29dMePu3rxamrEY6Rp+mvdU3J4IyFBEqUabcgQIDdXWmM/Pt7/n5v4B/7sCSEutLTIzLi0FDh6VNpjx8TKyvR+b5d5MjJcZ8ZZWTJzVq37jDoxkTPnSMRmE9EQHy/fk97icIiwMXr+lCnvoNFbWFmpe5uKi8V6IiNDBE5enm5Dh7paTk7kevOshKKGkAiivV2EypEjYkePSjoDZUePyuzXV9LTXWewubmes92cHBEu9JyQQBAdLcI4MxMYPdq31zQ16Z7FykpplcdReR9V296ue4bMav0Zx5GbCxQU6JafL21hoRQ2zsqicPc3vMwQEkY0NQGHD+szTtVXIqa83HNbsBmJiXIBVrNONRM1zkzphnfD4ZDMnWVlcjc75RRO1UMEFWc1cmT352maeIGUt9JoRu9mebl8HY4eFVu71vz94uNF5BQVidAZNkz6w4aJ5eVxMtBb+M9FSAjR2SlC5eBB4NAhvVVWU9PzeyQk6LNF4+xR9fPzJS6FM8hesHgx8POfyx1MkZ8PPP20bLUkYYHNpsdzTZjg/byuLvHyKO+nsS0pkQlGWZkEV+/bJ2ZGTIz8LocPd7URI8To6fHEpmm+zNvCg4aGBqSlpaG+vh6p3P5EgpSODuDAAWD3brnYHTig25EjPQfdpqe7zviKivSZYGGhxKvwQuhHFi8GLr7Ye2a8t96isCEedHSIZ0d5UY2e1cOHxYzlesxQ3qURI6QdNQoYM0ZsyJDw+p37ev+mqCHEIurrgV27dNu9W+zgQXFdeyMhQZ+tuc/ghg0TLwsJEA6H/KMbPTRGbDbx2Bw6xKUo0iucTlnWKi729MoePCiCqLu7d2oqMHasCJxx43QbOTI0l7QoakygqCFWcPy4BBQq27lTRMyxY95fk5wsF6TRo+UiZLRwm4H1mkDHrnR0uEZXG23XLml74l//Em8OIX6irU0Ez8GDuid3/35gzx455s2jGxsr15Vx42QJTdkJJwR3wkKKGhMoashA0tQkgmX7dmDbNml37JB7rzfy8vQZ1NixepubG+HCxRv+jl3RNNnrayZYjhyRAAhfo6t7orAQmDtXtylTJNkLIX6mvV0EjvL+Gr3BLS3mr4mJEbEzcSIwaZLeDh8eHOUqKGpMoKgh/sDhkJnQV1+5WndJvgoLgfHj9VnR+PEiXrhU1Av6ErvS2urdy6Ksra3nvx0frwclGa22Frj99p5fb7N5jttuB6ZPdxU6eXk9vxchfcTpFJ2+a5fuNVYe5KYm89ckJso168QTdZs0SbbMB5KwFDWfffYZHn/8cWzcuBFlZWVYsmQJLrjgAp9fT1FDektjo3hdtmwR27pVPDDeZjs5OfosR9m4cSzL0W96il0BpDDQFVfoIqakRJKO+EJurqdgUVvEuouuVuPyFuCgYmq++grYuBFYt072965dK4LIHeXNmTNH2qlTe+/N4dZy0ks0TX4uyrusPM07d3pPsjl0qAicKVN0Gzly4L5qYSlqPvjgA3z++eeYPn06LrroIooa4lcqKoDNm8U2bRIRs3+/+bnx8SJYTjwRmDxZFzJZWQEdcuSwYgWwYEHfXpuUZO5lUTZ0qHhN+oryIAGuwqY7D5Kmyda2tWt1obNtm2cgRG+9OdxaTvxIV5fE6mzb5uqVPnTI/PzERLkmTp2q28SJ/slnFZaixojNZqOoIX1C0yRId+NG3TZv9h64m5cns5DJk8WmTJGtk5z8BpDXXgMuv7zn8771LeCss1xFy6BBAx+gZCYmCgqAp57yXUw0NgLr17sKHbPEQwUFriJHeXO4tZwEiIYGETpbt4pt2SKPW1s9z42JkeX2adNEn0+fLtfRxMTe/k2KGrS3t6Pd4DtraGhAQUEBRU2E0dYmwmXNGv1+YRa8a7NJoNzUqfIDVC5Vel8sxOkEli6VuBVfKhMuXw7Mnz/gwzLF38s+miauQrVctW6dTJPNvDnTpsldxVtgBLeWkwHG4RDn45Yturd782ZzXR4dLd7tOXOAefPERozofu5BUQPggQcewIMPPuhxnKImvCkvBz7/XETMmjUiaNyTWEVHu84epk2T2UNysjVjJm5omoiZBx+UqyRgHmyriJSbdlOTpzenutr311sp+kjEoWJ1Nm0SU57xigrPc7OzdYEzbx4wY4brqjBFDeipiQQ0TfIyrF6t24EDnudlZwMnnaR77KdN6737kwQATQPeeQd44AGZ5gFASoos7YwaBVxzjX6eIpKXVzRNvvB/+APwl7/0fP7rrwOXXTbw4yKkG44edY2Z37hR0kEZsduBmTOBk08WmzixAcOG9SxqQjCvoO/Y7XbY+xMASIKOri5Zw/3sM7HVqz0nqjabuDZPOklX/cOHM+9LUKNpwLvvipjZtEmOJSeLmLntNiAjQ44pgeMeCNub2JVwwmYTsXfppb6JmmDOrkYihvx8Cf9S8fVtbfKzX7NG97JXVuoTVUAmpr4Q1p4adxgoHHp0dAAbNsjml88+ky+8e9hAfDwwe7au6OfOZf6XkEHTgPfeEzGzcaMcS04Gbr4Z+MUvzJNhcMuyJz1tLVfExwM/+xlw1126UCQkyFDhZEYP/JgxDXjnnTBbfmpqasL+/+2xnTp1Kv7whz9gwYIFyMjIQGFhYY+vp6gJfjo6gC+/FBGzcqWIGPeI+rQ0ES+nnir3s+nTmZg15NA04IMPRMysXy/HkpJ0MTN4sKXDC0m621quaZLtcfduOZaWBtxxh3i9GEhGQoCamgYMHhxmombFihVYYJKr4qqrrsKiRYt6fD1FTfDR1SWemOXLxVav9hQxgwcDp50mIua00yTvQaRPzEMWTQP++18RM19+KccSE4GbbpIdTtxq1j+621p+4YXA++8Dv/yl7KICxKd/773Aj3/cv1w9hAwwYR8o3BcoaoKDAwdkxeHDD2VJyX05KStLNmjMny8iZvx4xsOEPJoGfPQRcP/9wBdfyLHERODGG8VjQDHjP3pannM6gTffBO67T4+qHzZMhObll3PGQIISihoTKGqsobNTrrHvvSe2Z4/r8+npImAWLAC+8Q2KmLBC04CPP5Yb5tq1ciwhAfjpT4E77/Q9+o/4n85O4KWXZNu8Stw0fjzw298CF1zAHyEJKihqTKCoCRw1NRIy8c47strQ0KA/FxMjMTHnnAOcfrokuAuGKrDEj2gasGyZeGbWrJFj8fG6mMnJsXZ8RKelBfjjH4FHHwWOH5djs2YBjzwiswxCggCKGhMoagaWvXuBt98W+/xz18SnWVkiYs49FzjjDO5OCls0Dfj0U/HMqL2Y8fHA9dfLjpshQywdHumGujrgiSeAJ5/UK7YuXAg8/LAkDCHEQihqTKCo8S9Op4RHLF0qpjZWKCZNAs47T2zWLHpjwp7ly8Uzs2qVPLbbdTGTm2vt2IjvVFQADz0EPPecnor7ootkWWrcOGvHRiIWihoTKGr6T3u7rCr85z/ikTGmu46JkbiY888XIVNUZNkwSSBZsUI8MytXymO7XXbT3H139xWlSXBTXCz/r6++KjOYqCjgyivlGH/cJMBQ1JhAUdM3GhtlJ+iSJdI2NurPpabKstK3vw2cfTaXlSKKzz4Tz8yKFfI4Lk4XM0OHWjo04kd27pRt30uWyOO4OPHA/epXroHeTIpIBhCKGhMoanzn+HHxxvz737J5xViXIzdXNkdceKFsuWbiuwhj1SqZrX/6qTyOiwN+9CPgnnsk/zkJT778UnLcLFsmj5OSgFtvlfxCy5aZl694+unILF9B/A5FjQkUNd3T2Sk7lV55RXYtGYXM6NEiYi68UGIGGR8TpnQ32/78c/HMqJtabKwuZgoKrBszCSyffCLiRmWCTk72TDYFRHahUeJ3KGpMoKgx56uvgJdfBl57Daiq0o9PmCB18r7zHeaOiQjMstHm5wM33CBLTB9/LMdiY4Frr5Ubmw/lSUgYommyHPWrX3nuEDBis8l36NAhLkWRfkFRYwJFjU51NfD668CiRcDmzfrxnBzgBz+QeMDJky0bHgk0qm5Qd5eDmBhdzDBQlADitVu4sOfzli+XDJuE9BFf798xARwTsRiHQzLVv/SSbMFWuzXj4mTH0tVXA2eeKfcuEkE4HOKh6U7QJCUBW7cCI0cGblwk+Kms9O08lbGYkAGGt68I4MABETKvvAKUlurHp00DrrkGuOwyIDPTuvERi1m1ynXJyYzmZqCkhKKGuOJr/iHmKSIBgqImTGlrk51LL7yg77gFRLxcfrmsIpx4omXDI8GEr7NozraJO6ecIjEzpaXePX2JiZJ9k5AAQFETZmzbJkLm1Vf1Mi42m5Qm+OEPZZnJbrd2jCTI8LV0AWfbxJ3oaNm2ffHFcqExEzYtLcBZZ0nc1uDBgR8jiSi4MTcMcDjEKzNvnnhfnnlGBE1BgaQTKS6WrdqXXEJBQ9zo6gLeeKP7c2w2+TKdckpgxkRCi4sukm3b7gkXCwokaV9qqixxzpolifwIGUC4+ymEaWsTj8zjjwP79smxmBjxxvzoR+Kd4S5K4pXmZgmoeucd/Zj7bJu5RoiveMtxtHOn1E05eFAEzptviueGkF7ALd0mhIuoqa8H/vIX8fqWl8ux9HTgpz8FbrqJhZCJD1RWyo3myy+livbrr4uYcc9TU1AAPPUUBQ3pH9XVkvDqs88kc+eTTwI338zkV8RnKGpMCHVRU1Eh95c//xloaJBj+fnAbbcB110niT0J6ZF9+6RQ14EDEjn+zjvA3LnyHOv3kIGio0NqRr38sjy+/npZK4+NtXZcJCRgnpoworhYlpheekmWnADJ8HvnnbJ6wNpLxGfWrRMPTXU1MHy4BFuNHq0/Hx3NJGlkYIiLA158ERg3DrjrLuC550Rg/+tf4momxA8wUDiI2bULuOoqYNQo8c60tQGzZ0vivG3b5DkKGuIzS5cC3/iGCJoZM4C1a10FDSEDjc0G3HGHVMtNSpKMxHPm6EGBhPQTipogZMsW2ak0YQLwt7/JisDChVIUee1aCQRmQUnSK/70J4mLaW0Fzj1Xkhfl5Fg9KhKpnH++FEgtKAD27pXZmqr6Tkg/4K0xiNi4UX7rU6fKZhNNAy64QGI5P/4YWLCAcXWklzidwN13SwS50wn8+Mf6LJkQK5k8WS5uc+ZIDoozzwT+7/+sHhUJcShqgoCyMilXMGOGxGxGRUmszLZtUgh35kyrR0hCkvZ24IorgMcek8cPPSRxDCzuRYKFIUOk2OVll0nOpJ/8BLj1VnFPE9IHKGospKNDAoDHjJFq2YBUyN61S3bYTpxo6fBIKFNXJ7lAXn9dRMwrr0h1bbr6SLARHw+89hrwm9/I46eeEpe12uJJSC+gqLGIDz4AJk2SHUyNjZJsc9064O9/Z+wm6SclJcDJJ0vcTEoK8P77wJVXWj0qQrxjs0n24X/+E0hIkO/svHnAoUNWj4yEGBQ1AWb/ftlRe845Eh+XkyNpG9aulVg5QvrFV19JjMKOHUBenuSc+eY3rR4VIb5xySWSoC83V77Ds2ZJQDEhPkJREyCam4Ff/Up2NL37rqwI/OIXwJ49wNVXczcT8QPLlomH5tgx+aKtXSvBmISEEjNmSADx1KmSfuAb35B6MIDE2qxYAfzjH9Iy9oa4wYjBAUbTpDjtrbfKqgAgNZmefhoYO9basZEw4tVXgWuvlWDL+fMlwnzQIKtHRUjfyM8XL+OVV8oF9MorZdfel1+6lvHIz5eLKct4kP9B/8AAsnu37FK8+GIRNIWF8vv8738paIif0DTg4Yflot/VBXzve/IFo6AhoU5SkmQb/uUv5fHixa6CBgBKS+UCu3hx4MdHghKKmgHA6QR+/3vgxBMlv0xcnMTA7doFXHghN6AQP9HVBdxwg6xrAhJ1/tprgN1u7bgI8RdRUcD/+39ARob586p04S23cCmKAODyk9+pqZHyBe+9J4/POUe8o6NGWTsuEmY0N4tX5t13RSU/84wk2CMk3Fi1Cqit9f68pokrfNUq1i0jFDX+ZPVqySF19KhMlp96SnJJ0TND/EplJfCtbwHr10uOj9dfFxcgIeFIWZl/zyNhDUWNH3A6JWnrffeJB3T0aEm3wI0nxO/s2ydJ9Q4eBDIzJQX13LlWj4qQgSM317/nkbCGMTX9pKpKlph++UsRND/4AbBhAwUNGQDWrhUBc/AgMGIEsGYNBQ0Jf045RXY5defyLiiQ80jEQ1HTDz7/XFIpfPihJMF88UXZWZuSYvXISNjxn/9Ivo6aGikGtnYtU0+TyCA6WgITAe/C5vLL5TwS8VDU9AFNk91Np50mOwrHjJH0Cddey/gZMgD86U+Sh6OtTWJpli8HsrOtHhUhgeOii4C33gKGDnU9rqrNP/sssH174MdFgg6Kml7S3CwxmbffLstNl10m8ZosPkn8jtMJ3HWX7GrSNIk6X7JEv5ATEklcdBFQXCyi/vXXpa2ulh1PTU1SBLO62upREothoHAvaGyU+JnVqyX3zDPPAD/+Mb0zZABob5f6GW+8IY8ffhi4+25+2UhkEx3tuW37rbekRtTBg5KI76OP5AJNIhJ6anykoUGyA69eDaSlSdkRbtcmA0JdnXzZ3nhDioT97W/APffwy0aIGWoXYEoKsHKl7tkkEQlFjQ80NMgu2rVrgfR0qRvITSdkQDhyRIpSrlwpF+kPPgCuuMLqURES3IwfL5MAmw3461+BP/7R6hERi6Co6YH6epk0K0HzySfA9OlWj4qEJVu3ilresQPIy5MMqQsXWj0qQkKDc84BHn9c+rfcIstQJOKgqOkGJWjWrZPSI8uWAdOmWT0qEpZ88onk2Th2DJgwQb50THZESO+47TaJRXM6gUsvBfbssXpEJMBQ1Hihrg444wzgiy90QTN1qtWjImHJ3/4GnH22RKLPny+BWwUFVo+KkNDDZgOeew6YN09mpeefDxw/bvWoSAChqDFBeWi+/FIXNFOmWD0qEnZoGvDQQ1IBtatL8gP897/AoEFWj4yQ0MVuBxYvBgoLgb17xWPT1WX1qEiAoKhxw+kEvvtdETSZmcCnn1LQED/gcMiWuX/8Q9r2duD664F775Xn77oL+Pvf5YJMCOkfOTnA228DiYmytHvbbVaPiAQI5qlx449/lLIH8fHAxx8zrIH4gcWLgZ//XMq3K+LjJUOwzSbZUG+80brxERKOTJ4sE4WLLpLf2IQJkoeDhDX01BjYsQO4807pP/EEY2iIH1i8WBKCGQUNIIIGAO64g4KGkIHiwguB3/5W+jfdJF5SEtZQ1PyP9nbg+9+X9uyzgZ/+1OoRkZDH4RAPTXeJwP7xDzmPEDIw/PKXwPe+J3E13/mOZB4mYQtFzf+4917gq6+AwYOBl15i8lbiB1at8vTQuFNSIucRQgYGm00u6jNmALW1wHnnSUZVEpZQ1ECCgX//e+m/+CIwZIi14yFhQlmZf88jhPSNhARg6VJJarlzp7jlOzpcg/fpMQ0LIj5Q+Phx4MorZYXgxz+WtAaE+IXcXP+eRwjpO3l5wH/+A5x6KvDee7K9talJfz4/H3j6aQksJiFLxHtqfvYzoLQUOOEE4A9/sHo0JKw46SSZIXrDZpMke6ecErgxERLJzJypB0waBQ0gN4KLL5bgfhKyRLSoOXQIeO016f/970BSkrXjIWHGffcBra3mz6mgraeeAqKjAzYkQiIahwP45z/Nn1MB/bfcwqWoECaiRc3zz8v3+IwzgFmzrB4NCSuefx547DHp33yzuLaN5OcDb71FVzchgaSn4H1NY/B+iBOxMTVtbcALL0if27eJX/ngAz33zIMPAr/+NfDkk3KhLCuTGJpTTqGHhpBAw+D9sCdiRc2//gXU1EhIw7nnWj0aEjZs3gxccom4r6++WpagABEw8+dbOTJCCIP3w56IFTV//rO0P/kJEBOx/wrEr5SUAN/6FtDcDJx+uixBMeERCRUcjvD3Jp5yiiz9lpaaJ8W02eR5Bu+HLBEZU7NlC7BuHRAbC/zwh1aPhoQF9fXAOecAx45JjZm33gLi4qweFSG+sXgxMGwYsGCB5HBZsEAeh9tOoOho2bYNmE84NI3B+yFORIqaF1+U9jvfYaI94gc6O2XJaft2+UK9/z4waJDVoyLEN7zVJwvXLc4XXSSTjqFDPZ8bNQq44IKAD4n4D5umdVeYJrxoaGhAWloakpPr0dSUipUrJQ8TIX1G04Af/UjSsCclAZ99BkybZvWoCPENh0M8Mt52BKnlmEOHws97YVxus9slC2tzM/DKK9InQYW6f9fX1yM1NdXreRHpqWlqkt/n3LlWj4SEPA8/LIImKgp4800KGhJaRPIWZxW8f9ll4r359a/l+N13A42Nlg6N9J2IFDUAUFQkMTWE9JnXXpNKqADw7LPcRkdCD25x1vn5z4GRI+WzPvyw1aMhfSRiRc3IkVaPgIQ0K1cC11wj/dtvZ7IjEppwi7OO3a7XyvnDH4ADB6wdD+kTISdq/vSnP2HYsGGIj4/H7Nmz8eWXX/bpfUaN8vPASOSwa5cEE3Z2SiClyhxMSKihtjj3lHpgx47AjMdqzjtPUsx3dMhkhYQcISVq3nzzTdx22224//77sWnTJkyePBlnnnkmKisre/1e9NSQPlFRIVu36+okKOtvf5N4GkJCke62OBsf33QTcOut4V8TyWaT7N/R0VLR+5NPrB4R6SUhdTX+wx/+gOuuuw7XXHMNxo8fj+eeew6JiYl46aWXev1eFDWk1zQ3y0yuuFhcfW+/3X0VbkJCAW9bnFV9soceksdPPQVceKFndetwY/x4vczJLbcAXV2WDof0jpARNR0dHdi4cSMWLlz49bGoqCgsXLgQa9euNX1Ne3s7GhoaXExBUUN6hcMB/OAHwPr1QGam5KIZPNjqURHiHy66SMT68uXA669Le+iQJPP65S9lZ198PPDOO7Jk1d2OqXDggQfkd75jB/Dcc1aPhvSCkBE11dXVcDgcyMnJcTmek5OD8vJy09c88sgjSEtL+9oKCgq+fs7pHNDhknDjttuApUslmHDpUuCEE6weESH+xbjFef5817w0l14qQic7W1Kyz54NbNpk0UADQHo68NvfSv/Xv5ZCgSQkCBlR0xfuuece1NfXf20lJSVfP8fAduIzTz8NPPOM9F99FTjpJGvHQ4gVzJkDfPGFlAE5dkw8NkuXWj2qgeO664ATTwSOHwfuv9/q0RAfCRlRM3jwYERHR6OiosLleEVFBYZ4qXVgt9uRmprqYor9+wd0uCRcWLJEAiQB4He/k3IIhEQqw4YBn38uO4RaWiTG5g9/kCR9DgewYgXwj39IG+pBxcYg6r/8Bdi2zdrxEJ8IGVETFxeH6dOnY9myZV8fczqdWLZsGeb2ITUwPTWkR774QuJoNA24/npu8SQEANLSgPfek9+EpgG/+AVw5pmS0TTcCmLOny9pG5xOSc4XOVWFQpaQETUAcNttt+Gvf/0rXnnlFezatQs33HADmpubcY1KgtYL6Kkh3XLwoOx0am2VLdzPPttzLg9CIoWYGODPf9aT1X38sRTANBIuBTEff1xi6ZYvlzibcPFEhSkhV9Dyj3/8Ix5//HGUl5djypQpeOaZZzB79myfXqsKYgH1KCpKRXHxgA6VhCq1tcC8ecCePcDUqVKkMjnZ6lEREnw4HEBOjvdA2nApiHnJJbK93Uh+vixPXXSRNWOKMHwtaBlyoqY/GEVNVFQqWlpEgBPyNe3tEi/w2WdAQQGwbh2Ql2f1qAgJTlaskKWmnli+XJZyQpHFi8Xj5H6rVJ7bt96isAkArNLdDWlpskT62WdWj4QEFU4ncO218sVITZW4AQoaQrwT7gUxHQ7vsTTq2C23cCkqiIhIUfPd70r75z9bOw4SZPz615J4LCYG+Pe/gUmTrB4RIcFNuBfEXLWq+0SDmgaUlMh5JCiISFHzwx9K+/bb8n0kBC+8oKeD/7//AwyZqwkhXvClIGZqKnDyyYEbkz8Jd09UGBKRombsWFnedTrl/kUinI8+ku2pAHDffUAfdtMREpF0VxBT0dAgtZRCsYZSuHuiwpCIFDUA8NOfSvvXv0qVeRKhbN0qQYAOB3DFFcCDD1o9IkJCC28FMQsKJCuvzSazx4sukoR9oURPniibTT7nKacEdlzEKxErai64QMR1RYUkjSURSGkpcO65QGOjuO5eeIG5aAjpC94KYv7f/0l8miqGefrpQHW11aP1HV88UU89Fdrb1cOMiBU1sbHAj38sfQYMRyANDSJoSkuBceNk22ZcnNWjIiR08VYQ88ILgU8+kSKR69ZJ7bRDh6wcae/w5okCxOXP7dxBRcSKGkA8o9HRsoN3+XKrR0MCRmenVB3eulWqDr//vlxwCSEDw0knSc2owkJg715Jbrl5s9Wj8h13T9S118rxnTstHRbxJKJFzdChImwA4MorpRgrCXM0TYIWP/wQSEwE3n1XatQQQgaWceOAtWul8nV5OXDqqVJeIVQweqJ+/Ws5tmIFcOSIlaMibkS0qAGkrMeoUZKK4MYbrR4NGXAee0yiw202qeEyc6bVIyIkcsjLE9f4ggVAU5PUVfv73+W5UKryXVQEnHaaTJJee83q0RADES9qkpPlNxUdLb8lfj/DmDfeAO65R/pPPw2cf7614yEkEklLAz74QDweXV2y6/DKK8VjGkpVvq+8UtpXX2X17iAi4kUNAMyeDdx/v/R/+lPg8GFrx0MGgFWrgKuukv6ttwI332zteAiJZOx2mU3+4hfy+NVXPTP3BnuV74svll1du3YBmzZZPRryPyhq/sc990jsWkODTByC2fNJesmePbKHv6NDdmI8/rjVIyKEREXJcnBamvnzwV5bKTVVrisA8Le/WToUokNR8z9iYmSykJwsk3re98KEykpZt6+tFZecWmskhFjPqlVAfb3354O9ttIVV0j7j3/IrkpiORQ1BkaMAJ59Vvr33Re8vyPiI62tEjdz8KD85779tux4IoQEB6FeW+mMMyQtRFWV7KgklkNR48ZVVwGXXCLxa+ecA6xebfWISJ9wOIDLLwe++EJy0Lz/vlx8CCHBQ6jXVoqJkcBmAPj970Nj51aYQ1Hjhs0GLFokRZqbmoCzzqKwCUnuvFPPErx0KTBmjNUjIoS440uV78zM4K6tpDINr1gROju3whiKGhMSE2WlYuFCoLlZhA2XokKIP/4R+MMfpL9oUXBfEAmJZHyprVRTIwHFwbhtevFimUC5E+w7t8IYihovJCSIsPnmN0XYnH225IwiQc7bbwM//7n0H35YcmEQQoIXb7WV8vOB886T/q9+BfzoR8EVjOtwyLXGTGwF+86tMIaiphsSEmTl4swzdWGzcqXVoyJe2bBBRIzTKRfAu++2ekSEEF8wq/JdXCyTlD/9SbZ/v/SSXITr6iwe7P9Ytcozt46RYN+5FabEWD2AYCchAfjPfyQdwYcfSvDwu+/KsimxEIdDLhZlZRJEWFAAfOtbQEuLqNA//7n7dXpCSHChaiu589OfSozKd78LLFsmxTHfe8/6mm2hvnMrTKGnxgfi40XYnHWW3DPPOQf473+tHlUEs3ixZ0r1sWOBigoplvfPfwKxsVaPkhDiL845RyYxQ4dKZew5c4Avv7R2TKG+cytMoajxkfh4YMkS4NxzgbY2aX/zG1npIAFk8WIJwHN3+3Z1SXvTTZLpkxASXkyZAqxbB0yeLBOY+fPlogxYUwyzp51bNpt4kLlRIaBQ1PSC+Hi5p157rYiZX/9aJhBVVVaPLELoLjAPkIvIb37DwDxCwpX8fPHYnHOOJNf8zneAq6+2phhmdzu31OOnnmIG8wBDUdNL4uKAF18EXn5Z4m0+/BCYOhVYs8bqkUUADMwjhKSkyA6OG2+U3/wrr1hXDLO7nVtvvSXPk4DSK1GzdetW/Pa3v8Wf//xnVFdXuzzX0NCAa6+91q+DC2auvlqS1Y4ZI7+fU08Ffvc7LkcNKAzMI4QAksn3qaeCoxim2rn1f/8nj9PTgUOHKGgswmdR89FHH2HWrFl444038Nhjj2Hs2LFYvnz518+3trbilVdeGZBBBiuTJgHr18suYocDuOsu2YDD5agBgoF5hBDF6tXBUwwzOhr49relX1fH2a2F+CxqHnjgAdx+++3Yvn07iouLceedd+L888/HfyN8G1BKCvDaa8Bf/yoxNx98IPFsTNQ3AJxyiqeb1wgD8wiJHILNczt4sOy61DR6iy3EZ1GzY8eOr5eXbDYb7rzzTjz//PO4+OKL8e677w7YAEMBm01yvX35pewsPnZMYtV++1vGrPqV6Gj5BzaDgXmERBbB5rmNigLy8qTfXewfGVB8FjV2ux11bpkcv//97+OFF17Ad7/7XSxRW+siGLUcdeWV4n287z7g5JOBTZusHlmY8MILknzLZpNZkREG5hESWfhSDDMmBkhKCtyYlCf5zTdZrdsifBY1U6ZMcYmhUXzve9/DCy+8gJ/97Gd+HViokpwswfiLFkl/3TpgxgzghhuA2lqrRxfCbNggOWgAcYGVl7umVGdgHiGRhS/FMLu6ZGb5xz8OfEHMxYuBzZul/8wzrNZtET6LmhtuuAGlpaWmz1122WVYtGgRTj31VL8NLNS56ipg924JItY04LnngNGjJfaGMWS9pLpa8lG0twPnny81nVRK9csuk5ZLToREHt62VBcUyOzygguAjg7g5pvlGnL8uH6OPxP2qaSgra2ux1mtO+DYNK138nX58uVY4KXw0fPPP4+f/OQnfhnYQNDQ0IC0tDTU19cjNYBZZ1esECfDjh3yeOZM4NlngdmzAzaE0MXhkERbH30EjBol63uDBlk9KkJIMOFeC+6UU2Sio2lysb39dqnwPWwY8MYbIjZ+/nPX2Jf8fPH89Nbj63DI+3qLo7HZ5L0PHeLkqx/4fP/WeklcXJx2++23ax0dHV8fq6qq0r71rW9pgwYN6u3bBZT6+noNgFZfXx/wv93RoWlPPqlpqamaJr80TbvqKk0rKwv4UEKL++6Tf6yEBE376iurR0MICUXWr9e0ESPkWhIVpV+EjWazif3737177+XLzd/P3ZYvH4hPFjH4ev/udUbh5cuXY8mSJZg5cyZ27tyJ9957DxMnTkR9fT22bNnSZxUW7sTGSh6oPXuAa66RY6+8IktSTzwhHlLixrvvStkDQNbtJk2ydjyEkNBkxgzZsXHxxd7X//uasC/YtpZHOL0WNfPmzcOWLVswceJETJs2DRdeeCFuvfVWrFy5EkVFRQMxxrBiyBDgpZckgHjWLKCxEbjjDrlfv/++1aMLIvbvBy6/XPo33QT84AfWjocQEtqkpQE//Wn35/QlYV+wbS2PcPpU+2nv3r3YsGED8vPzERMTgz179qClpcXfYwtrZs8G1q6VGlLZ2cDevVL5+8wzpfxCRNPSIkF99fXA3LnA739v9YgIIeFAeblv5/nqVXE4xDIyvJ/DpKABpdei5tFHH8XcuXPxzW9+E9u3b8eXX36JzZs348QTT8TatWsHYoxhS1SU1JDau1fi2GJjJR52zhzgm9+M0KzEmgZcfz3w1Vei9v71L6kiSggh/cVXb0l2tt73tktq8WIJEF640Hu+DiYFDTy9DdYZMmSI9v7777sc6+jo0G6//XYtLi6ut28XUKwMFPaF/fs17ZprNC0mRo8tO+UUTfvgA01zOq0eXYD485/lg0dHM7COEOJfuro0LT9fAoK7C+odNUrTXn5Z0958U843Ppefr2l33NHzewCaVlDQ+8BjYoqv9+9eb+murq7GYPdsrv9j5cqVOO200/wgtQYGq7Z095biYuCxxyT2RgUQT50K3HOP7DYMW8G/bp2UO+/sBB5/XNxXhBDiT1ROGcA1IZ/NJo+Tk4GmJu+vV+d1R2amZBVmDi2/4ev9u9fLT94EDYCgFjShxLBhwF/+Ahw8CNx2G5CYKIkqL70UGD/eVeyEDZWVcqHp7JR4ml/8wuoREULCEW8J+/LzgX//W+JpHn1U4gPM8MUPUFMjYoaCJuD0KVCYBIahQyVG9sgR4P77gfR0ib/54Q+BESPkucZGq0fpB7q6gO99TxJijR0r0dPd1XMhhJD+cNFF4hI3K7WSnCw7Ofqb+p1buC2BoiYEyMwEHngAOHxYctrk5sr9//bbgcJC4Fe/AioqrB5lP7j3XrmoJCeLazglxeoREULCne5KrfhDkHALtyVQ1IQQKSmyKnPokBSsHjMGqKsDHn4YKCqSopl79lg9yl6yeLEEEAGyrjZunLXjIYSQ/ggSbuG2FIqaEMRulyWonTtFE8yeLbUen3tOVm9OPRV49VXP2mpBx549sqcdkOChSy6xdDiEEAJABEl+fu+XwbmF23IoakKYqCjgwgslid+KFcB558mxVauAK68E8vKkOO3WrVaP1ISmJlm/bmwUFfboo1aPiBBChOhoKW4JeAobm03sjjtE+BjJz5cg5N4WxSR+o9dbukOZUNnS3R+OHgUWLZLlqcOH9ePTp4t357LLgqDItabJQN58U9y8mzZJ/QhCCAkmFi/2rOZdUCCemIsu8l4dnPgdX+/fFDVhitMJfPKJ1IFculR2SgNAfLzsmL72WomN87ZrcUB5+mkpGhcTIy6mk06yYBCEEOIDFC5BAUWNCZEkaoxUVQGvvQa8+CKwfbt+fNgw4KqrxIYPD9BgVq0CvvEN2cb99NPAz34WoD9MCCEkVKGoMSFSRY1C04ANG2ST0euvAw0N+nOnnQZcc414cZKTB2gAZWXAtGlSVO6yy0RpMR8NIYSQHqCoMSHSRY2RlhbgP/+R+JtPPtGTZCYlibC58ko/Z/ju7AROP108NRMnSkmEpCQ/vTkhhJBwhqLGBIoac0pKZAv4okXAvn368bw8iYX7znf8sIx8223Ak08CqanA+vXA6NH9HTYhhJAIgaLGBIqa7tE0caD87W/AG29IYj/F4MHA+efLFvKFCyXg2GfefFPKIACym+DCC/05bEIIIWEORY0JFDW+094OfPyxaJClS4HaWv255GTg7LOBCy4Azjmnhy3iO3ZIdsDmZuDuu4FHHhngkRNCCAk3KGpMoKjpG52dEgqzZIlYaan+XEyMxN58+9viySksNLywoQGYOVOqcJ5+OvDf/8oLCCGEkF5AUWMCRU3/UTuolMDZvdv1+alTRdyc9y0N0x6+GLYliyXL5qZNQFaWNYMmhBAS0lDUmEBR43/27gXefluWqNaskaR/ijyU4ltR7+O8352K0386BgkJ1o2TEEJI6EJRYwJFzcBSVQW8+y7wzkuV+Gh1IpqhJ7xJSJCce+eeK+ayTEUIIYR0A0WNCRQ1AeDoUWDaNLRVNWDFwofwzgm34Z13bSgpcT1twgQRNwsXSpWExERrhksIIST4oagxgaJmgOnokNTE69YBU6bIelRCAjQN2LYNeO89sbVrXZepYmNlg9SCBeLNmTOnl1vGCSGEhDUUNSZQ1AwwN90E/OlPssd740ZgxAjT02pqgA8/BD76CPj0U3h4ceLjRdjMny8aiSKHEEIiG4oaEyhqBpBXX5XaCoAE1px7rk8v0zTg4EFg+XKxTz+V0lBG4uJE2Jx2GnDqqcDcuaywQAghkQRFjQkUNQPEV1+J6mhtBX79a+DBB/v8VpoG7NkDrFwptmKF1ME0EhMDTJ8uAueUU4CTTwbS0/v3EQghhAQnmgaUlDSgqCiMRM1DDz2E9957D1u2bEFcXBzqjDn8fYSiZgCoqwNmzAAOHADOOku8NH6rgilf5v37Rdx89pnYkSOe502YIOJGWVERC4ATQkgo0t4uqc1Wrxb7/HNg5swG/Pe/YSRq7r//fgwaNAhHjx7Fiy++SFETDDidUivhnXdERWzcCGRmDvifPXxYMhwrkbNnj+c5eXmyq2rePLEpU2QZixBCSHBRVSUbSNasEVu/Hmhrcz0nN7cBZWVhJGoUixYtwi233EJREww89BBw772A3S5Sevp0S4ZRVSU/BKXqN2wAurpcz4mPl4oNc+eKzZ4N5OZaMlxCCIlYurqkJODatbJRds0aYN8+z/MGD3b1vo8c2YCsrJ7v32FdiKe9vR3t7e1fP25oaLBwNGHGRx8B990n/T//2TJBA0j1hW9/WwwAWlqAL790Vf61teLdWbVKf92QITLs6dOBadOkxENBAZetCCHEH7S3i4DZvFkc+Zs2AVu3enphAGD8eN2zPm8eMHq067XY19t3WIuaRx55BA/2I2iVeOHwYeCyyyTg5brrgGuvtXpELiQmynbw+fPlsaZJOYfPP5eZwdq1wM6dsstK5c5RZGaKuFE2ZYr8uPwYJkQIIWFHfb3sGdmyRUTMpk1yne3s9Dw3NRWYNUv2l8ybJ62/NntYuvx0991347HHHuv2nF27dmHs2LFfP+7N8pOZp6agoIDLT/2hrU22HG3YIC6O1atDMolMc7PMGNTsYfNmmVG4L1sBUuJh4kQROFOmAJMnA5MmyQ+TEEIiCU2Tea0SMFu3SnvwoPn5GRn6JFF5xkeOBKKievd3fQ0fsdRT84tf/AJXX311t+eM8JLAzRfsdjvsdnufX09M+NnPRNBkZAD//ndIChpA8twoN6eirU13lW7apP9gW1okcG39etf3GDYMOPFEsUmTxE44QbacE0JIqFNXB2zfLvbVV7o1NpqfX1Agkz61nD91qtT5C+SSvqWX36ysLGRlZVk5BNIbXnwR+Otf5Rv6j3/IjqcwIj5en0koHA7Zra4EzubNUvLh6FGguFjs7bf18+PigHHjROBMnCg2YYL8sHs7MyGEkEDQ0gLs3i2Tuu3b5Rq3fbtntndFbKzEwJx4oqsHOwCbX3skZOaUR44cQW1tLY4cOQKHw4EtW7YAAEaNGoXk5OTuX0z6z8aNwI03Sv83vwHOOMPa8QSI6GiJqRk9Grj0Uv14ba388NXMZetWWT9Wy1pbt7q+T1KSiJ0JE8TGjZOLQlER43UIIYGhuVnEy65dcr3asUPs4EFZVjIjP18mZ5Mn657pMWNE2AQjIbOl++qrr8Yrr7zicXz58uWYryJCe4BbuvtITY0k2CsuBs47D/jPf+h2MMHplH8iNdPZtk0uGHv2mAfLAeIdGjNGRM64cdIfO1aWsVi5nBDSWzQNqKiQ687u3bqI2bXLPHGpIjNTJlwTJ7p6mgcNCtjQu4VlEkygqOkDDofUcfrwQ4nu2rAheL7lIUJXl2RFVrOinTvlArNnj2x5NMNmkyWrMWPkn91oI0aw9hUhkYymye7NAwfEy3LggNi+fXJdqa/3/tqsLPESGz3H48cD2dnBnc4iJAKFSQjw//6fCJqEBAkMpqDpNTEx4n0ZOxb4znf04w4HcOiQ7go2zqyOH5cdBocPm79ndraIm+HDPS0/n9mTCQl16urk93/okNjBg3r/0CEptecNm02uBWPHunqCx40LjriXgYSeGuKd994DvvUt6b/6KnD55daOJ0LQNKC6WsTN3r36TEy1tbXdv95mA4YOld1ZRUXSFhaKFRVJS08PIdahaUBlpYiWI0fEDh+W5WvVdudtASQCoKhIJjfKgztypAiZUaNCdmOqV7j8ZAJFTS84eFC2AdXVSYDwH/9o9YjI/6ir85y5qf7hw+bZOt3JzJTtlwUF4tlR/YICEURDh4pzjhDSOzRNwhBLS2WXZEmJmLFfUuJ96dlIVpYuXIYPd/XOFhUFb7DuQEBRYwJFTTc4HFJDoKxMUjvedZds65kzB1i5kusZIYKaAart5mrWZ5wN+ppuPCNDFzhDh0qRUKPl5gI5OczLQyKHpia5RB475mmlpbr5IlhsNvkdKS9qYaEuVpSXlR5VHYoaEyhqvLB4MfDzn8tUwkhqqkS25udbMy4yINTXi7jxNossLZW8Fb5gs0nhudxcqaWlhI67ZWfLedy+ToKN1lbZLVRRIRMC1a+okGDcsjK9bW72/X2zsnQvqNEbmp8vAmboUM4VewMDhYlvLF4MXHyxeZKChgapDElRE1akpen5JszQNBE+R4/qLnQ1GzXOUsvLxcFXVSX21Vfd/12bTZa9srJE5GRliQ0e7GmZmeIpSk4O7h0ZJLjo6pLl2ZoasepqV1Pf1aoqETBVVb0TKoB4T4YOFQFv9Frm58vx/Hx5zGT21kBPTSTjcIif091Do7DZ5Bd66BCn2MQDh0NuHGoma5zVus94a2q8J/fqjthYETdK5KSne9qgQeJUTEuTVllKisQFURSFDg6HLPE0NoqwbmgQU/3jx82tpkYC6H0oCWiK3e7qVVR95X0cMkTvM9erNdBTQ3pm1SrvggaQu1BJiZznY4JDEjlER8sNIDtbso12R1eX3HiMM+TKSjE1o1ZtVZX0OzokaaESRn0dY3KyCBxlSUlyzNgmJUmyQ9Uqi48XYWS0+Hi5CcbHi8XFRYZwcjgkCL29XW9bW3Vra9P7LS1izc2u/aYmz7axUTdflz17IjXV3Ps3eLDuJTR6C1NTI+P/MBKISFHzm98AF14IzJ4d4Q6IsjL/nkeIF2Ji9NmvL2ia3OBqa/VZeE2N+Sy9rs5zZq8K7jkccryn7bH9JS5OhE5cnKvFxuoWE6P3o6PlsbGNjpZtuu6mbrY2m27q30i1RnM6Pc3hEGHp3nZ2ihn7nZ0iKDs6RLio1uEY2H9DIzExrp63tDQRpGaeOqMnT3nzImlXEHElIkXNE0+IZWRICaNzzgHOPFOUe0SRm+vf8wjxEzab7kEpKOj96x0O8QQoD4DRI9Dc7OktMPMstLSYeyGUl8KIEgGRQlSU7sVy92bFx3t6vhISPL1jqjV60ZTZ7fSckL4RkTE13/lOPT79NBXHj+vP2WySluWss4Czz44QL47DIYKlqsr8ecbUEGKKpukejLY2MXcPR3u7d2+Iw2HuPTHzsKi/594aPTiqNfP0REWZe4WMniPVj4kx9zjFxenLbXY7t/GTwMMt3SYY/1ESE1PxxRfA+++L/a/o99ekpwPf/KZ4cM48U6Law46qKsmhbVR3CnWlfOst4KKLAjsuQgghxABFjQnd/aOUlUmJo//+F/joI8/7/MSJIm7OOgs4+eQwSEHtdMq624cfyp5Em0327yoKCoCnnqKgIYQQYjkUNSb4+o/S1SXpWZTIWb/edTtqQgJw6qkSj3PGGVLlNOTWfx96CLj3XvkwX3whZVpVRuHcXOCUU7jkRAghJCigqDGhr3lqamqATz4RgfPhh56bgYYMkR3P8+cDp50mKzpBLXJWrABOP128NS+9BFxzjdUjIoQQQrxCUWOCP5LvaRqwc6csUX30kZRFci8Bn5Mj4kbZ+PFBJHIqKoApUyRD2lVXAYsWWT0iQgghpFsoakwYiIzCbW3AunUiblasANau9dzuOXiwrOaceqqInBNPtGhlx+GQwKBly0RpffklK6YRQggJeihqTAhEmYS2NtEKRpHj7slJTQVOOkmEzimnADNnBqhOyIMPAg88IIkj1q8XYUMIIYQEORQ1JlhR+6mjA9i4UUTOZ58Bq1fr2U4Vdjswa5YInJNOAubNk3o2fmXZMtmjrmnA3/4GXHGFn/8AIYQQMjBQ1JgQDAUtu7qkmvGqVbpVVrqeY7PJjqqTTxaRc9JJUneyz3E5ZWUSR1NZCfzwh8ALL/TzUxBCCCGBg6LGhGAQNe5oGrBvn4ibzz8XT86+fZ7n5eaKB0d5cqZOlSyfPdLVJR6aFSuASZNk+3ZCgr8/BiGEEDJgUNSYEIyixoyKCmDNGhE4q1cDmzdLanUj8fHAjBnA3LkSkzNzJlBUZOLNue8+4Le/lUIrGzbIfnNCCCEkhKCoMSFURI07ra2iRz7/XMTOmjWSO8edrCwROspmNq9A7g++Ie6g118HLrss8IMnhBBC+glFjQmhKmrcUUtWa9bIatL69RKn4+7NAYA8lGJ6UTWmXzMZ06cD06ZJVQRCCCEkVKCoMSFcRI0ZbW3A1q2y02r9F05seKsYO1uK4IRnQpwhQ/C1wFFWUBBECQIJIYQQAxQ1JoSzqHHhnnuARx9Fc3IONv91AzZW5GPjRhE8u3dLdQR3MjNF3EydKjZlCnDCCSz/RAghxHooakyICFHz/vvAuedK/5//BC65xOXp5mbdo7NpkwQh79ghm6TcSUwEJk8WgaNs4kQ5TgghhAQKihoTwl7UlJSI8qitBW68EfjjH316WVsbsH27CJxNm4AtW0T4uGdCBoCoKPHgTJkigmfyZCn7MHQol68IIYQMDBQ1JoS1qOnslMJSa9dKwMznn/er9oLDIcHImzeLbd0qYsc9UaAiI0PEjbJJk4Bx44CUlD4PgRBCCAFAUWNKWIuaO+4AnngCSEsTd8uIEQPyZ8rLdU/Oli3Atm0Sp+NwmJ9fWCglpsaN09tx40QEEUIIIb5AUWNC2Iqad94Bzj9f+osXAxdeGNA/39YG7Nol28q3bpWlrG3bRAB5IztbFzhjx+pWUCBLXIQQQoiCosaEsBQ1hw/LdqXjx4Gf/xx46imrR/Q1tbUidnbsAHbulP6uXRL6443ERGD0aEl8bLTRo7mURQghkQpFjQlhJ2o6OqS095dfSpnvVat8LAhlLY2NwJ49InB279Zt3z7zBIKK3FwRN+42YkRIfGxCCCF9pKqqAdnZPd+/YwI4JuJv7rpLBM2gQcCbb4bMnT0lRS/lYKSrCzh0SMTOnj3A3r3S7tkjAcplZWIrV7q+LipK6l6NGiU7s4zt8OH9ipcmhBASADRNvPv794vt2+faTpvm2/vQUxOqLFkCXHSR9Jcu1WNqwpTjx0Xk7Nvn2u7dCzQ1eX+dzSZxOiNHisgZOVJsxAhp09IC9xkIISSScTiA0lLg4EHgwAFp9++X/v79QH2999eOGNGAgwe5/ORC2IiagwdFttbXA7/4hex6ilA0TaqaG1W9sgMHuhc8gOzCGjFCbPhw17awEIiNDcznIISQcKCuTjzuBw9Kq/oHDwLFxRI10R1Dh8qE84QTXD3vWVkNyMujqHEhLERNeztw0kmSEnjuXFmL4Z3XFE0Dqqp0d+b+/a4zBG85dxRRUfIDGzZMBE5RkbSFheL9KSigp4cQEjk4HLKrtaRE7MgR2aui2uJiETXdERMj19SRI2UCOWqUbsOHe89Y7+v9mzE1ocbtt4ugyciQOBoKGq/YbLJ1PDsbmDfP8/nGRplFHDigzyiMM4y2Nv3H643UVF3g5Od7tvn53LVFCAl+HA6Z6B09qltJid6WlMjSkVlJHXeys0WgGL3fw4eLkMnPF2EzUNBTE0r861/ApZdK/733gHPOsXY8YYxa1jp0yHUmcviw/gM/fty390pJEY/P0KHyg1b9vDzdcnKoTwkhA0NTkwiSY8d0Ky0VO3pU2rIy3wRLdLRcswoKPD3Yw4fL4+Rk/38Gbuk2IaRFjQr/bmyUXU+PPmr1iCKe5mZXN2xpqT6zUbOb7gLfjCivUm6uuQ0ZorcJCQP7uQghwY/aLVReLoJEte527FjPsYWKqCi5zrh7m/Pz9WX3IUMG1tPiDYoaE0JW1LS1SfzMli3AyScDy5db860ivUbNkIx29KhcbNTMydcZkiI1VS4sOTmuNmSIvtyWkyNtUhILjRISKjgcIlQqKmQpqLJS+kYrL9f73eX1cic11dU7nJfn6jnOz5frRrDeWhhTE07ceqsImsGDgTfeCN5vHfEgOVnPiuwNp1MCmo0zK+NMq7xcn4W1tQENDWJ79/b89xMSgKws7zZ4sJjqDxrEMhWE+Iv2dqC62tOqqsytulquB70hI0P34iqPbl6eq6c3L29gloSCEd4dg51//AN47jmZbv/97yKpSVgRFaV7W6ZM8X6epomYUSLHbPZWVaUfa20VO3JEzNexpKcDmZmelpHhaenpYmlpFEMkfGlvlxg6ZbW1nlZT42rV1bJE3VtsNvm9ZWfLZMPdI6ssN1fOYXJRVyhqgpk9e4Af/1j6v/wlcOaZ1o6HWIrNJuIhLa17z4+iuVl3YbvPCCsrPWePDQ0yS1QX5b6MTYmcQYM8LS1NXOCqTU2VIOqUFOknJVEYEf/T0SGhiMqUp1NZfb1YXZ2rGUVMa2vf/350tIgU5Q1VfWVKvKj+4MF0xvcHxtQEK62twJw5Uvr6tNOATz7hN50MKB0dnrNNZcbZqHF22t8LvjvJybrQSU72tKQk3YyPExPNLSFBt+ho/42T+A9Nk9iQlhbdu9jSYm5NTSLWlanHTU2uZhQxPSV78xWjcDfzXJp5NzMz6cX0F4yp6YaWFpkZBjU/+5kImuxsWYKioCEDTFycvgbfG9xd88ePe85+1TH3WXJDg9x4HA55L3VTKivz96eTz5eQAMTHm5vdLmbs2+3yurg4135srJixHxsrP9OYGNd+dLRnGx0tNzr31mbTW2NfYRb0raalmqab0+nadzrl39i97erybI3W2am3nZ0iEIx9d2tvd7W2Nte+uykR09s4kr6QkKB7BY2ewrQ0755F5XlMT5fzKYyDn4i8U+blARMnAjNn6jZpUhDVg/z734EXXpAr2Ouv9/4uQ0gAsdv1IMW+oGlyg1NLA42NnjNvZcbZuTI1i3fvt7bKzVShbry+brMngScqSvesKQ+cahMSPL11ytw9e+qYcYmT88LIICKXn4B6AK6umrg44MQT9erRM2YA48dbkBBt1y754y0twP33Aw88EOABEBI+OJ26N0AtayivQWur3nrzMHR2Smv0RBg9FkbPhdGzYew7HJ7eEG+eE3dPi/JgGL0xqlVeG2PrzdPjzTNk9CYpc/c6Kc+TmWdKea+MXiz12N3jpTxi7t4y4zJhXBxTEBBzmKfGBPWPsmtXPXbvTsWGDcD69WJm2WHtdmDyZGD6dN0mTBhAodPcDMyeDezYAZx+OvDhh/R3EkIIiXgoakzw9o+iaVKIa8MGV2to8HwPu12WqqZN023SJJlx9JtrrgEWLRI//pYtsm+PEEIIiXAoakzoze4np1MKHW7cqNumTebr8dHRslQ1daqInKlTJd9Ir4KRFy0SURMVBSxbBsyf34sXE0IIIeELRY0J/d3SrWlSwXnTJt02bvSe02PYMInTmTRJb084wSRgbft2YNYsWdz/zW+Ae+/t9dgIIYSQcIWixoSByFOjaVK4cPNmVyspMT/fbhevzsSJInImjWrFxDvOxtADK2E74wzggw+Y1IAQQggxQFFjQiCT79XWSpqZbdv0dts22X1hxiBbHSbOSsKEKbGYOFFEz4QJkmWSEEIIiWQoakywOqOw0wkcOiQiZ/t2YPvbB7FtQxv2YjQcXlIGZWWJuDHa+PGSSpsQQgiJBChqTLBa1Ljw1VeyfbutDe2/+R12n3cHduz4n9jZLru6Dx70/vLsbGDcOBE448fr/SFDmOeBEEJIeEFRY0LQiJrGRkmwt3cvcM45wDvvmMbRNDdLLr4dO8R27pS2uNj7W6elicBxt2HDmPKGEEJIaEJRY0JQiBpNA77/feCNN4D8fIkq7uVaUlOTFPDeuVO3XbtkC7q3GipxcbLzauxY3caMEbPaaUUIIYR0BwtaBivPPy+CJiYGePPNPgXHJCfrGY6NtLUB+/aJwNm9W9pdu0QAtbXpHh93hgwRcTN6tNioUWIjRkgKc0IIISQUoKcmkGzeDMydKwVkHn8cuP32gPxZpxM4ckSEjtH27AHKy7t/7dChusgZOdLVBg0KyPAJIYREOFx+MsFSUVNfL66VAweA884Dli4Nioje+noJ7dmzR2zfPhnivn09VzPOyNAFzogRejtihIghxvAQQgjxBxQ1JlgmajQNuPRS4K23gKIiSUWckRG4v98HNE1y7ezfrwsdZfv3A5WV3b8+NlaCk4cPF5EzfLhuw4YBmZlBoekIIYSEAIypsRqHA1i1CigrA9atE0ETGytxNEEuaAARHJmZYrNnez7f2Chbzg8eFKGj2gMHgMOHgc5OEUP79pm/f3KyLnCMVlQkbUYGRQ8hhJDeERKipri4GL/5zW/w6aefory8HHl5ebj88svxq1/9CnFxcVYPz5PFi4Gf/xw4etT1+OWXmyuEECQlBZg8Wcwdh0M++qFDInZUW1ws/bIy2cGlsiybkZQkAkdZYaFrPzfXpIYWIYSQiCYkbgu7d++G0+nE888/j1GjRmH79u247rrr0NzcjCeeeMLq4bmyeDFw8cWyfuPOokXAt74FXHRRwIcVSKKjdQFiVmy8tVUClw8dEqFz+LC0ysrLJUeP2q7u7W8MHSoCp6DA3AYPpreHEEJCiY4OoLRU6icazdeNwiEbU/P444/jL3/5Cw52l3bXjQGPqXE4ZO3E3UOjsNkkN82hQ4yi7Ya2NhE9R46I4DGa+oJ3dvb8Pna7/HPn54vIUf2hQ3XLzqbHhxBCAkFzM3DsmIgWZSUlcss8elT6FRXmr50ypQFbtoRxTE19fT0yeohNaW9vR3t7+9ePGxoaBnZQq1Z5FzSAXtJ71SpzFwYBAMTH6zlzzHA6xZujhE9Jid4qq6iQnfMqzscbUVFATo4sZ+XmAnl5el/ZkCFiwbjSSQghVqJpQEODhBWUl0ur7Ngx176vt2A1IVVedxV+8OMf9/zakBQ1+/fvx7PPPtvj0tMjjzyCBx98MECjgvzP+fM8YkpUlIiPvDxgzhzzc5QL0zgDKCnRjx07Jj9Ah0P/0fVERoaInJwcETnubXa29LOyJCacEEJClaYmmRwarbzcsy0rE++6ryQmipdcec2NXnTVNwsdaGjwTdRYuvx0991347HHHuv2nF27dmHs2LFfPy4tLcVpp52G+fPn44UXXuj2tWaemoKCgoFbflqxAliwoOfzli+npyYIcDiAqioROmYzCzXzKC/3bbnLSGamCJzsbE/LytLbrCxJYmhS+osQQvxGR4dc74xWWelpFRXStrT07v1TU3XPtjev99ChssmkL7GOIZGnpqqqCjU1Nd2eM2LEiK93OB07dgzz58/HnDlzsGjRIkT18k4QsJia0lLzQGHG1IQkTidw/Lg+K/E2Y6mokAuFt/pb3oiOlpmJEjmDB+uPBw8WgaRa1U9KYhA0IZGKwyHXpOpqoKZGTPWrqqRfXa33q6p6TqZqRmKiTM6UmXmolfd6oEvqhISo6Q2lpaVYsGABpk+fjr///e+I7oMoCEjyPbX7CXAVNuoO9NZbYb/7KZJxOuXCoty1VVX6zMdoaqbU1zCvuDgROBkZuthR/fR06StLT9ctNZViiJBgobNTxImy2lq9NZoSLqpfV2c+b+6JqCiZFBk9xsrU0rkSMNnZkk8sWAgrUVNaWor58+ejqKgIr7zyiougGTJkiM/vE7CMwmZ5agoKgKeeoqAhLrS36wLHfXal+u4zMcOKaq+JipLlLiVyBg3SH6t+WppuxsepqWJ0MhIitLWJB6ShQdq6OmmV1dV5mlHENDf37++npXl6cpWH193rm5Ulv/NQXeoOK1GzaNEiXHPNNabP9Wb4AS2TYMwonJsLnHIK7wak32iarHVXV+uzNuNMzn2WZ5z99SaYrzuSk0XcpKXJ+rgSO6qfkmJuycmeZrfTc0QCh9MpQqKpydMaGz2tocGzVQKmoUHiVPxBWpqrh1X109M9PbGqn5ERWRsSwkrU+AvLq3QTYiFtba6zRDVrdJ9Fms00Gxr65yHyRlSUxAclJ0ublCRr82aWkKC3ZhYfr1tCggim+HjXNiaGIiqY0DT5XrW3y/dTtUZrbdX7LS3y2N1aWsytudnVWlsH5nMkJ+teTffW6AVVx4zLwmlpnO/6Ams/dcPnnwOzZoniJSRSiI/XdyH0hfZ2faaqZqvG2avRjDNf1TfOitXNxenUzwsENpuIG7td4pKMfXeLjRUz9pXFxOitu0VH6627RUXprZnZbLoZHxvH746almqapzmdemtmDoeYse9wAF1dnm1Xl8SAGPtG6+hw7Ruts1MXLx0der+3uwr9RVSU7i1MSvL0KKq+8kIaPZHKS2k8HqpLOuFIRIqac86RNicHmDBBt/HjxSh2CPHEbtfX5vuLw6EvA6hZdFOTPrv2Nvt2n50bZ/HufTXr7+rS/66m6eeQ4EN51Ox27x44oxk9eO5ePeX1Ux5AZSkp8l702IUnESlqCgr0rLMVFcCnn7o+n52tC5zx44Fx46TNyeEPgRB/EB2tz3QHGofDdYnD6CkwegzcvQtGz4O7KW+F0WPh7uXo7PT0gCjz5j0xeleUKdz7Zh4co6fHaEbvkPICKa+Ru7l7m1Rr5qFy92AZvVvuXi8lVtw9ZUrIxMXx+kr6T8TG1ERFpWLnTmDHDrFdu6R4YnGx99cPGiQCx2hjx0pqGq6JEkIIIQMDA4VN8OUfpakJ2L1bFzpK7Bw86D2pmt0udYrGjnW10aODa58/IYQQEopQ1JjQn91PbW3Avn0icHbv1gXPnj3d7woZOlQEzpgxrlZYyOAyQgghxBcoakwYiC3dDocsWe3ZI2LHaFVV3l9ntwMnnKBXox49Wh6PHCmpp7m2TAghhAgUNSYEOk9NTY2IHXfbv7/7rYxJSSJuRo2SVtmoURLkzPgdQgghkQRFjQnBknyvqws4fBjYu1dszx5Z2jpwQI53VxAxNlYCk0eOBEaM0FtljOEhhBASblDUmBAsoqY7OjpkOWv/ft0OHBA7dKjntNxZWSJuhg/XW2UFBZGVVpsQQkh4QFFjQiiImu5wOIDSUhE4Bw+Kqf6BA1Ljpzuio4H8fF3kDBvmakOHcmmLEEJI8EFRY0Koi5qeqKsTb86hQyJ0jG1xcc+1e2JixJtTVCQip6jItZ+fLwmyCCGEkEBCUWNCuIua7nA6gfJyXeCoVtmRIz3XYbHZpG5QYaGInMJCT0tP584tQggh/oWixoRIFjU94XAAZWUidg4fdjUlenypl5OUJN4eb5afL7VXCCGEEF+hqDGBoqbvaJrk3Tl8WASOEjwlJfK4pASorPTtvVJSJH7HaHl5Yqo/ZAiDmgkhhAgUNSZQ1Awsra3A0aOuQsdoR48C9fW+vZfNJju5cnN1wZObq9uQIXobHz+wn4sQQoi1+Hr/jsgq3WRgSEiQrMgnnOD9nMZG4Ngx2cVVWqr3jx3T+2VlEt9TWSm2dWv3fzc9XcSNMiV2cnJc28GDubuLEEKCiZYWoKJCrLxcb8vL5V6g+uPG+fZ+FDUkoKSk6PWvvOF0SjbmY8fkS+3eGq2jAzh+XGzXru7/dlSUCJucHFfLztZbo9EDRAghvUPTZCeumpQqU8KlosL1cWOjb+/ra2JZLj+RkEXTRMwoJe+u7o3Kv6pKzu8NKSmyBGa07GwRRuqxsZ+UxJ1fhJDwwuGQHGjV1XIdrapy7VdViUgxPtfTTlp34uNdPes5Oa6hBkOGACkpDZg4kctPJIyx2YCMDLHx47s/t6tL//GZzRjcZxUdHTKDaGyUXD++YLeLyFGWmelp6nhGhrRpaazWTggJDO3tIlBqa8UbbmbV1a52/HjvJ4SAXNvcvd/u3nFlqak9TwgbGnz7uxQ1JCKIidGVf09omvyAlIfH22zE2La1yQVDxQr5SlSUxAQpcaZMHUtP924JCfQMERJpOJ2y4UItu7tbba1nq0RMc3Pf/+6gQeYeauXBdn9st/vtI/cKihpC3LDZZJaRlgaMHt3z+ZomFws1yzHOdozH3K25WY8fqqnp/Tjj4uRCk54u7aBB+rjdLTVVzNhPSaEwIiSQOBxAU5NMmoxWX6+3RmtoEGFSVyd2/Lgc60/QiHEiZeZRdvc2Dx4s54ZKig2KGkL6ic0mQWzJyZJp2Vfa2+UipUSNcVblPtsyWl2dXBw7OvTlsr4SHS3iRomc1FT5HCkpnqY+o7slJeltUpJ4xQgJdTRNfqNNTTIBMbZmpparzayhQdr+eErcSUgw9+CaeXuVYMnICP8lb15+CLEIu10PgusNmiYXSOWCNs7izGZ67q0yQMSRer0/P1dioi5ylCUmmltCgt4a+/Hxrq3qK7PbKaAiDU0TMd/W5mqtrZ5ta6tsF3bvt7R4WnOzmHvf4RiYzxEba+5BNbbKlBfW6JEdNMi65Z1gJyIvCb2NzCYkmLDZ9IthQUHf3sPplAu3mkEaW7NZp7eZqXEGq24A7e26F2qgiY7WBY7d7tpXFhfn2jdabKzeuveVxcR4tu4WHd29RUW59qOi5P/R2Ffm/ti4PGi2VKiWIjSte3M6xYx9h8Oz9WZdXebW2enZKuvo8HysTD1W3xdj32gqXk31rSA+3tUjaea5NHo0jX3jcq9q7XYu+w4UESlqsrOBkSMlXmL0aD1h3AknyE0inF1zhADyHVcXXn+gXPVK5JjNfr3NkNVM2n1mbZxxG2fhXV3633U49L9DIg8lYpUnz+jNM/MCJiR4eg3VMXevohIxiYn0CIYSEZmnBqgHYL7P3W4XwaNEzqhRepufT8FDiNV0demz9tZW77N7NfN39wC4ewyM3gR3z4KZB8LotXDvu3s2vHlDjN4S5T0ZaJRXyOglMnqRjN4kMzPzTnnzZJl5vty9ZOo5bx41M8+bcUkyLo7ejkiCZRK6YedOScq2d69u+/ZJPpL2dnl+507P1ynBM2qUbupxYSHVPCGBQN1Uk5KsHol/8bZsZHze2DdbljIuV3lbwiIknIlIT403pdfVJYUY9+0T279fTAkeo9vbnZgY2fkycqSrjRgBDB/uPzc/IYQQEmmwSrcJ/SmTYBQ8Bw6IKdFz4IB4eLojMxMYNkwEjrJhw3RLSOjjhyKEEELCHC4/+ZmYGPG6jBjh+ZzTKcUWldgx2qFDrgnXNm40f/+cHBE3RUWebVGR78W8CCGEkEiFnpqA/F2guFgEjrLDh/W+L1VKMzN1gaOssFCsqEiyPnLdnBBCSDjC5ScTgrFKtyrTroROcbFu6nF9fc/vEx+vi5zCQtmabuwXFMjWREIIISTU4PJTiGCz6emtp00zP6e+XgTO4cMS12PsHzkClJXJFla1k8sbGRmyLV2JnIIC/XF+vhhjewghhIQq9NSEAR0dwNGjInRKSsSOHJFWHfNliQuQZa6hQ0XgGFujpadzqYsQQkjgoKcmgoiL8x7ErKiv1wWPsqNHxdTjlhY9oPmrr7y/V0ICkJcngicvT2zoUL2flwfk5nK5ixBCSGChqIkQVHG0iRPNn9c0XfiUlorYUa3ql5ZK1ejWVn13V09/MzdXbMgQvTVaTo4EOTNTMyGEkP5CUUMAyHKSqv46aZL381pbJYZHiZxjx/TW2G9t1StF797d/d+OjgayskTgKKFjtOxsvT94MDM3E0IIMYe3B9IrEhJ6XurSNNnGfuyYCKDycmkrKvS+amtqpBZOebnY1q3d/32bTQKeldjJzhZB5K1NT6cXiBBCQoH2dqCqSqyy0rVNT/ftPShqiN+x2fTlrnHjuj+3s1O+sOXluuipqBCrrHTtV1WJYFJxP2b1udyJipLg56ws3QYPNrfMTGmTkhgITQgh/cHhAI4fB6qr5XpdXe1qVVV6q/rdbWiZPt23v0tRQywlNlYPLu4Jh0N+HJWVulVUuKp5Y7+uTrI9q+O+EhenixyjZWR49jMydIuL6/M/AyGEBCWaBjQ1STxlTY20xr4xY77Rjh/vW/X5mBi5/rp73QsLvWfkN8It3SRs6ez0nBEYW+OMQc0keqrh1R1JSSJu0tP11mjGY4MG6e2gQRREhJCBQ9OA5mYRGnV1YseP61Zb6/pYHVPHuyvm3BNpafok0egpz8ry9KJnZcn5Zp5ybukmEU9srL77yhc0Tba1G92lZrMR95mKmpE0N4uVlPR+rImJIm7S0ry37paaqrepqQygJiQc0TRJrlpfL7GKxlZZXZ3nY3VM9R2O/o3Dbvf0Tpt5sdUyvjoeG9vvf4JewcsgIf/DZhNvS1KS1NPyFadTn/kokWOc5ZiZ8aIDiJhqaZHg6r6SmKgLnJQUva8eGy05WW/dTf0bREf3fSyERCqaJglRm5pkktPU5GmNjXrb2Cgixb01Wn88JUZiY109xO7eZOVRNvM4JyaGRqwhRQ0h/SQqSr8QjBzZu9c6HHLROn7c+wzLOAMzmrrgtbbKeylhVF7un88VH+8qcoyWmOjad7eEBM9+QoKnBXoWRyIb5fVobfW0lha9de+3tIhAMfaVqcdGEdNfr4gZNpvrRMXMe6s8u0ZLS9OFTEJCaAiT/kBRQ4iFREfrM6G+0tEhszsldMxmempGaJwhms0gm5rE8wTIxb+tTZbhBoroaBFP8fFywVV9o9ntnq2ZxcV5trGx0iqLjdWPGdvYWFm+c2/D/QYwEDgc4lno7PRsOzqkNfY7Ojz7ytrb9bY7U9/VtjbPx62tro8DSVycp0c0KcnTc6rM3dOakqKLlaQkpqfwhYgUNddfD4wZI7lWhg+XdsgQfmFIaBIXp69l9xc1k1WzUDX79GZqNmucxZrNeNW56iajcDj09wpGoqJ0gaMsOtqzNVpUlGc/KsrTbDbXfnemMBNZaquHpnn2jeZ0ihn77uZw6K17X4kV99bdQmXrSXS07jHszsNo5o0081gavZqqzzi3wBOR/+T/+IfnMbsdGDZMRI7R1LGMDM7aSPhjs+kX+sGDB+ZvaJrMppXb331G3dqqz7bNZuHuM3T3Gb1qzWb+Zp4CZWY4nfrfIn1HiUN371hsrFx73T1qZl431Tfz1nnz7pl5/7j0Gd5EpKi57z4JyDx0CDh4UHartLcDe/aImZGcrIscdysqoughxFdsNv0G059lN3+ivBdK4KjlEndvhDpm5rUw82y4e0BUX/09oxfFzLti9Hq49808OEbPjtHTY/QMGY8ZvUjuniV3b5OZd8rowTKa+zIeveAkUDBPDeRCdfSoiBx3Ky6WdP49kZws4sZoSvAUFnJ5ixBCCOkrzFPTC2Jj9eUmM1pbgSNHdKFz+LBYcbFYebnEHuzYIebtbxQU6CLH3QoKZA2WEEIIIX2DosYHEhIksHjMGPPnW1tlCau4WBc8RistFW/QwYNi3khPB/LzReDk55tbSsqAfERCCCEk5KGo8QMJCcDo0WJmdHVJDI9R6JSUiB05Io8bG/XEbNu2ef9bKSkiboYOFTP2lWVlMXEaIYSQyIMxNUFCfb3E9Rw9KmLH2C8tlb7KPtsT0dESwzN0qBSKVK27paczuJkQQkjww5iaEEMlWJowwfs5TU26wCkt1c34uKJCdleox91ht4v4ycvTayQZbcgQaen5IYQQEgpQ1IQQycndx/YAstRVUSHLXUrYlJXJY2VlZXpFarUc1h1RUVL+fcgQXeio/pAhQE6O3nqrsEoIIYQMNBQ1YUZMjB5bM3Om9/Pa22XXlhI8xrasTH+uslJyaJSX+1ZTyG4XceNu2dmebUYGPUCEEEL8B0VNhGK36/l0uqOrC6iq0kWNEjuqX1Gh9xsaRCwdOSLWE1FRkrU2O1ssK8u1b7TsbCnIxlw/hBBCvEFRQ7olJkaPsemJ1lYROd6sslK3mhrxAKnHvhAdLfWNlNAZPFhM1T1SfeOx1FQKIUIICQU6OoDaWrk/1NRImIRqfU1nQlFD/EZCgl46oic6O+XLWlEhniCj4Kms1I9VVYk1NEgAdG9EEKBXwc7MlOUu1RotM1POycjQ27Q0Lo0RQkhfaGuT9CS1tWLGvtFqalxFTFOT9/ecMcO3v01RQywhNlYPNPaF9nZR68qqqvRW/SCMVl0tlZ8dDv01vcFmE2EzaJAIHXcbNEh/TvWNFh/PgGlCSGjidErutLo63Y4f9+yr3GpGq6sTr31fiYrSJ6JGr/uwYcCGDT2/nnlqSNjS3u46C1CzArPZgppJHD/e/WzBV+LiRNwoYaS27Kt+aqprq/rK0tKAxEQKI0JI7+jqEkHS0CC5zRoaXPv19eZWV+f6uL/KQIkT5QE3esyNHnIlWpSlpZmHDDBPDYl47Hbf44GMdHTID1yJHPcZiftMRbXqwqBp8h69XSpzJypKBE5KimfbnSUn662xHxdHkURIsOF0Ai0tMplqbHRtVd+bNTR4ti0t/hub3a5PxIxeamPrflwJmZQUa+IZQ0bUnH/++diyZQsqKyuRnp6OhQsX4rHHHkNeXp7VQyNhRlycvgurtzidciFSblpvsyBlxpmTmlE1NMj7OJ36+/iD6Ghd6CQnSwHVpCTPfmKi9FWr+t4sIUHa2FiKJhJ+OJ0SI9LSIssqLS3m1tzs2SpravLsK9HiTxFiJD5enwQpb7C7d9jdg6z66nF8/MCMbSAJmeWnJ598EnPnzkVubi5KS0tx++23AwDWrFnj83tw+YmEApomFzoleMxmZarvPpMzm+21tQVm3FFRusjxZvHxuhkf2+2efbvdu8XFefbj4mS3HoVV+OB0itdTWXu7mHu/rU1/rEwda2vTrb1dhInxWGtr9xao34/N5ullVY/NzJsXNy1N2ri4wIw7UPh6/w4ZUePO22+/jQsuuADt7e2IjY316TXqH6WkpB75+RQ1JDLo6nKdGTY3i+AxziSNs0jjLNM48zSbmba2yo0nmIiLE4uNFVN94zEzi4kRM/aVRUe79ruzqCjXvjez2cSMfW/mTkyM/L8a0TQ9DkL1jeZ0uraqbzSHQ2/d+2bW1aW33qyzU2/NrKPDs69EjMMx8N+X3hAXJ2Lc3XupjhnN6Ol094oavaWqn5BAQd4dYR1TU1tbi9deew3z5s3rVtC0t7ejvb3968f1/6sIWV3dADpqSCRhs+kzPH+i4oe8zXCNrbfZs5ppq35rqz4TV8fcZ+idnfpjd9QNMZyZOhXYvNnqUQSe6GjdMxcba+61i4/XW2NfnWP0Fho9g8pzaGzdbaDSPKjgXuKdhoYGAECPfhgthLjzzju1xMREDYA2Z84crbq6utvz77//fg0AjUaj0Wi0MLCSkpJu7/uWLj/dfffdeOyxx7o9Z9euXRg7diwAoLq6GrW1tTh8+DAefPBBpKWl4d1334XNi8/O3VPjdDpRW1uLzMxMr6/xJw0NDSgoKEBJSUnYxfCE82cD+PlCnXD+fOH82QB+vlBmID+bpmlobGxEXl4eorrZVmWpqKmqqkJNTU2354wYMQJxJhFPR48eRUFBAdasWYO5c+cO1BD7RTgHJofzZwP4+UKdcP584fzZAH6+UCYYPpulMTVZWVnIysrq02ud/4tONHpiCCGEEBK5hESg8BdffIH169fj5JNPRnp6Og4cOID77rsPI0eODFovDSGEEEICS0jUL05MTMTixYtx+umnY8yYMfjhD3+IE088EStXroTdbrd6eF6x2+24//77g3qMfSWcPxvAzxfqhPPnC+fPBvDzhTLB8NlCNk8NIYQQQoiRkPDUEEIIIYT0BEUNIYQQQsICihpCCCGEhAUUNYQQQggJCyhqAsSwYcNgs9lc7NFHH7V6WH6nvb0dU6ZMgc1mw5YtW6wejl84//zzUVhYiPj4eOTm5uKKK67AsWPHrB6WXyguLsYPf/hDDB8+HAkJCRg5ciTuv/9+dIRR8aSHHnoI8+bNQ2JiIgYNGmT1cPrNn/70JwwbNgzx8fGYPXs2vvzyS6uH5Bc+++wznHfeecjLy4PNZsN//vMfq4fkNx555BHMnDkTKSkpyM7OxgUXXIA9e/ZYPSy/8Ze//AUnnngiUlNTkZqairlz5+KDDz6wZCwUNQHk//2//4eysrKv7eabb7Z6SH7nzjvvRF5entXD8CsLFizAP//5T+zZswf//ve/ceDAAVx88cVWD8sv7N69G06nE88//zx27NiBJ598Es899xx++ctfWj00v9HR0YFLLrkEN9xwg9VD6TdvvvkmbrvtNtx///3YtGkTJk+ejDPPPBOVlZVWD63fNDc3Y/LkyfjTn/5k9VD8zsqVK3HjjTdi3bp1+Pjjj9HZ2YkzzjgDzc3NVg/NL+Tn5+PRRx/Fxo0bsWHDBnzjG9/At7/9bezYsSPwg/FLpUnSI0VFRdqTTz5p9TAGlPfff18bO3astmPHDg2AtnnzZquHNCAsXbpUs9lsWkdHh9VDGRB+97vfacOHD7d6GH7n5Zdf1tLS0qweRr+YNWuWduONN3792OFwaHl5edojjzxi4aj8DwBtyZIlVg9jwKisrNQAaCtXrrR6KANGenq69sILLwT879JTE0AeffRRZGZmYurUqXj88cfR1dVl9ZD8RkVFBa677jq8+uqrSExMtHo4A0ZtbS1ee+01zJs3D7GxsVYPZ0Cor69HRkaG1cMgbnR0dGDjxo1YuHDh18eioqKwcOFCrF271sKRkd5SX18PAGH5O3M4HHjjjTfQ3NxsScZ/ipoA8bOf/QxvvPEGli9fjp/85Cd4+OGHceedd1o9LL+gaRquvvpqXH/99ZgxY4bVwxkQ7rrrLiQlJSEzMxNHjhzB0qVLrR7SgLB//348++yz+MlPfmL1UIgb1dXVcDgcyMnJcTmek5OD8vJyi0ZFeovT6cQtt9yCk046CRMnTrR6OH5j27ZtSE5Oht1ux/XXX48lS5Zg/PjxAR8HRU0/uPvuuz2Cf91t9+7dAIDbbrsN8+fPx4knnojrr78ev//97/Hss88GdUFOXz/fs88+i8bGRtxzzz1WD9lnevN/BwB33HEHNm/ejI8++gjR0dG48soroQVxMu7efj4AKC0txVlnnYVLLrkE1113nUUj942+fD5CgoEbb7wR27dvxxtvvGH1UPzKmDFjsGXLFnzxxRe44YYbcNVVV2Hnzp0BHwfLJPSDqqoq1NTUdHvOiBEjEBcX53F8x44dmDhxInbv3o0xY8YM1BD7ha+f79JLL8U777wDm8329XGHw4Ho6Gj84Ac/wCuvvDLQQ+01/fm/O3r0KAoKCrBmzZqgLaja28937NgxzJ8/H3PmzMGiRYsQFRXc852+/P8tWrQIt9xyC+rq6gZ4dANDR0cHEhMT8dZbb+GCCy74+vhVV12Furq6sPIe2mw2LFmyxOVzhgM33XQTli5dis8++wzDhw+3ejgDysKFCzFy5Eg8//zzAf27IVGlO1jJyspCVlZWn167ZcsWREVFITs728+j8h++fr5nnnkGv/3tb79+fOzYMZx55pl48803MXv27IEcYp/pz/+d0+kEgKD2svXm85WWlmLBggWYPn06Xn755aAXNED//v9Clbi4OEyfPh3Lli37+mbvdDqxbNky3HTTTdYOjnSLpmm4+eabsWTJEqxYsSLsBQ0g300rrpEUNQFg7dq1+OKLL7BgwQKkpKRg7dq1uPXWW3H55ZcjPT3d6uH1m8LCQpfHycnJAICRI0ciPz/fiiH5jS+++ALr16/HySefjPT0dBw4cAD33XcfRo4cGbRemt5QWlqK+fPno6ioCE888QSqqqq+fm7IkCEWjsx/HDlyBLW1tThy5AgcDsfX+ZNGjRr19Xc1VLjttttw1VVXYcaMGZg1axaeeuopNDc345prrrF6aP2mqakJ+/fv//rxoUOHsGXLFmRkZHhcY0KNG2+8Ea+//jqWLl2KlJSUr2Og0tLSkJCQYPHo+s8999yDs88+G4WFhWhsbMTrr7+OFStW4MMPPwz8YAK+3yoC2bhxozZ79mwtLS1Ni4+P18aNG6c9/PDDWltbm9VDGxAOHToUNlu6v/rqK23BggVaRkaGZrfbtWHDhmnXX3+9dvToUauH5hdefvllDYCphQtXXXWV6edbvny51UPrE88++6xWWFioxcXFabNmzdLWrVtn9ZD8wvLly03/n6666iqrh9ZvvP3GXn75ZauH5heuvfZaraioSIuLi9OysrK0008/Xfvoo48sGQtjagghhBASFgT/4jkhhBBCiA9Q1BBCCCEkLKCoIYQQQkhYQFFDCCGEkLCAooYQQgghYQFFDSGEEELCAooaQgghhIQFFDWEEEIICQsoagghYUNZWRm+//3vY/To0YiKisItt9xi9ZAIIQGEooYQEja0t7cjKysL9957LyZPnmz1cAghAYaihhASMlRVVWHIkCF4+OGHvz62Zs0axMXFYdmyZRg2bBiefvppXHnllUhLS7NwpIQQK2CVbkJIyJCVlYWXXnoJF1xwAc444wyMGTMGV1xxBW666SacfvrpVg+PEGIxFDWEkJDinHPOwXXXXYcf/OAHmDFjBpKSkvDII49YPSxCSBDA5SdCSMjxxBNPoKurC//617/w2muvwW63Wz0kQkgQQFFDCAk5Dhw4gGPHjsHpdKK4uNjq4RBCggQuPxFCQoqOjg5cfvnl+O53v4sxY8bgRz/6EbZt24bs7Gyrh0YIsRiKGkJISPGrX/0K9fX1eOaZZ5CcnIz3338f1157Ld59910AwJYtWwAATU1NqKqqwpYtWxAXF4fx48dbOGpCSCCwaZqmWT0IQgjxhRUrVuCb3/wmli9fjpNPPhkAUFxcjMmTJ+PRRx/FDTfcAJvN5vG6oqIiLlMREgFQ1BBCCCEkLGCgMCGEEELCAooaQgghhIQFFDWEEEIICQsoagghhBASFlDUEEIIISQsoKghhBBCSFhAUUMIIYSQsICihhBCCCFhAUUNIYQQQsICihpCCCGEhAUUNYQQQggJCyhqCCGEEBIW/H9cidVP6etzlgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eta = 0.8\n",
    "show_trace_2d(f_2d, train_adam_2d(adam_2d))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "DLmMd9h4l4Aa"
   },
   "source": [
    "# AMSGrad\n",
    "\n",
    "[Video timestamp](https://youtu.be/UvM0hK4E2dc?t=1479)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "Khhsvs3Dl4Ac"
   },
   "outputs": [],
   "source": [
    "def amsgrad_2d(x1, x2, s1, s2 , t):\n",
    "    beta1, beta2, eps = 0.9, 0.99, 1e-6\n",
    "    g1, g2 = 0.2 * x1, 4 * x2\n",
    "    g1, g2 = 0.2 * x1, 4 * x2\n",
    "    s1[0] = beta1 * s1[0] + (1 - beta1) * g1\n",
    "    s2[0] = beta1 * s2[0] + (1 - beta1) * g2\n",
    "    s1[1] = beta2 * s1[1] + (1 - beta2) * g1 ** 2\n",
    "    s2[1] = beta2 * s2[1] + (1 - beta2) * g2 ** 2\n",
    "    m1 = s1[0]#/(1-beta1 ** (t+1))\n",
    "    m2 = s2[0]#/(1-beta1 ** (t+1))\n",
    "    v1 = max(s1[2], s1[1])\n",
    "    v2 = max(s2[2],s2[1])\n",
    "    x1 -= eta / (math.sqrt(v1) + eps) * m1\n",
    "    x2 -= eta / (math.sqrt(v2) + eps) * m2\n",
    "    s1[2] = v1\n",
    "    s2[2] = v2\n",
    "    return x1, x2, s1, s2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 315
    },
    "colab_type": "code",
    "id": "WmJEncF-l4Ag",
    "outputId": "b99469a0-f719-45e4-9d5e-fd11bcebf9df"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 20, x1 -0.977985, x2 -0.470241\n",
      "epoch 20, x1 -0.571139, x2 0.487553\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eta = 1\n",
    "show_trace_2d(f_2d, train_adam_2d(amsgrad_2d))\n",
    "show_trace_2d(f_2d, train_adam_2d(adam_2d), color ='green')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "mQQ1o7Yql4Al"
   },
   "source": [
    "[![Dataflowr](https://raw.githubusercontent.com/dataflowr/website/master/_assets/dataflowr_logo.png)](https://dataflowr.github.io/website/)"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "include_colab_link": true,
   "name": "Gradient_descent_optimization_algorithms_empty_colab.ipynb",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
